Students and Teachers Forum

1. The diagonal of the square is 6 cm. Find the area of the square.

Given,     Diagonal of square (d) = 6 cm     Area = ? We know, Area of the square   = 12 d2                                    .....

2. The sides of the triangle ABC are 6 cm, 8 cm and 8 cm. Find the area of triangle ABC.

Here, triangle ABC is an isosceles triangle. Let, the equal sides, a = 8 cm  and b = 6 cm So, Area of triangle ABC = b4 √(4a2 - b2 )                           .....

3. Find the area of a right-angled triangle whose base and height are a cm and b cm respectively.

Here,      height (h) = b cm and      base (b) = a cm We have,    Area of right-angled triangle (A) = 12 bh                             .....

4. Find the semi-perimeter of a triangle having sides 20 cm, 13 cm and 21 cm.

Let, a = 20 cm     b = 13 cm      c = 21 cm Semi-perimeter (s) = 1 2 (a + b + c)                     .....

5. Find the area of equilateral triangle whose side is 4 units.

Given,      Side of the equilateral triangle (a)  = 4cm      Area = ? We have, Area of equilateral triangle                 = √34 a2       .....

6. The diagonals of a kite are 12 cm and 8 cm. Find the area of the kite.

Given,     First diagonal (d1) = 12 cm      Second diagonal (d2) = 8 cm We know,  Area of kite    = 12 × d1 × d2                     .....

7. In ∆ABC, if a = 7.5 cm, b = 10 cm and c = 12.5 cm, find the area of ∆ABC.

Given,         a = 7.5 cm    b = 10 cm and  c = 12.5 cm Now, Semi-perimeter of ∆ABC (s) = 12 (a + b + c)                           .....

8. In ∆ABC, if a = 6 cm, b = 8 cm and c = 10 cm, find the area of ∆ABC.

Given,        a = 6 cm    b = 8 cm and     c = 10 cm Now, Semi-perimeter of ∆ABC (s) = 12 (a + b + c)                         .....

9. Find the total surface area of a prism having the triangular base of side 5 cm, 12 cm and 13 cm and height 8.5 cm.

Here       Sides of the triangular base,         a = 5 cm        b = 12 cm                  c = 13 cm        Height of the .....

10. The area of an equilateral triangle is 16√3 cm2, find its perimeter.

Let a be the side of equilateral triangle. Then, Area of an equilateral triangle = 16√3 cm2    Or, √34 a2 = 16√3    Or, a2 = 16⨉4    Or, a =√(16⨉4)       .....

11. In ∆ABC, if AB = 36 cm, BC = 48 cm and AC = 60 cm, find the area of ∆ABC.

Given, AB (c) = 36 cm    BC (a) = 48 cm and     AC (b) = 60 cm. Now, Semi-perimeter of ∆ABC (s) = 12 (a + b + c)                             .....

12. In ∆ABC, if AB = 11 cm, BC = 12 cm and AC = 13 cm, find the area of ∆ABC.

Given,        AB (c) = 11 cm    BC (a) = 12 cm and AC (b) = 13 cm Now, Semi-perimeter of ∆ABC (s) = 12 (a + b + c)                           .....

13. Find the total surface area of a prism having the triangular base of side 5 cm, 12 cm and 13 cm and height 8.5 cm.
 

Here the sides of the triangular base,      a = 5 cm             b = 12 cm                 c = 13 cm     Height of the prism (h) .....

14. The perimeter and the length of an isosceles triangle are 25 cm and 9 cm respectively. Calculate the area of the triangle.

Let, the equal sides of the isosceles triangle be a and the unequal side be b. Here, perimeter = 25 cm             Or, 2a + b = 25 cm             Or, 2a + 9 = 25 cm       .....

15. In ∆ABC, if a = 9 cm, b = 12 cm and c = 15 cm, find the area of ∆ABC.

Given, a = 9 cm    b = 12 cm and     c = 15 cm. Now, Semi-perimeter of ∆ABC (s) = 12 (a + b + c)                                 .....

16. In ∆ABC, if a = 3 cm, b = 4 cm and c = 5 cm, find the area of ∆ABC.

Given, a = 3 cm    b = 4 cm and     c = 5 cm Now, Semi-perimeter of ∆ABC (s) = 12 (a + b + c)                                 .....

17. The perimeter and the length of two sides of a triangle are 36 cm, 8 cm and 12 cm respectively. Find the area of the triangle.

Let, a, b and c be the three sides of triangle. Given,      P =  a + b + c = 36cm      a = 8cm      and b = 12cm Now, c = P - (a + c)             = 36 - (8 + .....

18. The longest edge of a right-angled triangle is 74 cm and one of the other edges is 70 cm. Find the area of the triangle.

Let,      The hypotenuse of the right triangle (h) = 74 cm      The base of the right-angled triangle (b) = 70 cm Now, The perpendicular of the triangle is given by, p = √(h2- p2 )    = √(742-702 .....

19. One of the sides of a triangle is 10 cm and its area is 60 cm2. If the triangle is isosceles, then find the measure of its equal sides.

Let a be the length of equal sides and b be the base of the isosceles triangle. Then,        The area of a triangle = 60 cm2    Or, b4 √(4a2-b2 ) = 60    Or, 104 √(4a2-102 ) = 60    Or, .....

20. The area of an equilateral triangular land is 900√3 square meter. Find the length of each side.

Here, Let a be the length of a side of the triangular land. The area of an equilateral triangular land = 900√3 m2 Or,   √34a2 = 900√3 Or,    a2 = 900⨉4 Or,    a  = .....

21. The edges of a triangular land area are in the ratio 12:17:25 and its perimeter measures 540 fts. What is the area of the land? Find it.

Let, x be any constant. Then, the lengths of the edges of a given land is given by 12x, 17x and 25x. According to the question,                Perimeter = 540 feet.          Or, 12x + .....

22. The longest edge of a right-angled triangle is 74 cm and one of the other edges is 70 m. Find the area of the land.

Here, Hypotenuse of the right triangle (h) = 74 cm Let, base of the right triangle (b) = 70cm Now, the perpendicular of the triangle is given by,                             .....

23. In a right-angled isosceles triangular land, one of the equal edges is 10 m. Find the area of the land and the remaining edges.

Let, perendicular = base = a = 10 m. Now, the area of the right-angled triangle is given by, Area = 12 ⨉ p ⨉ b         = 12 ⨉ a ⨉ a   [ since, perendicular = base = a.]        .....

24. The perimeter and one of the lengths of an isosceles triangle are 25 cm and 9 cm respectively. Calculate the area of the triangle.

Let, the equal sides of the isosceles triangle be a and unequal side be b. Here,      Perimeter = 25 cm Or, 2a + b  = 25 cm Or, 2a + 9  = 25 cm Or, 2a = 16 cm Or, a = 8 cm Now, the area of the isosceles triangle is given .....

25. A side of a triangle is 10 cm and its area is 60 cm2. If the triangle is isosceles then find the measure of equal sides.

Let, b be the base and a be the equal sides of an isoscales triangle. Here, the area of a triangle = 60 cm2 Or, b44a2-b2       = 60 Or, 1044a2-102   = 60 Or, 4a2-100       = 24 Squaring both .....

26. The edges of a triangular land area are in the ratio of 12:17:25 and the perimeter is 540 feets. What is the area of the land? Find it.

Let x be a constant. Then, the measure of the edges of the given land is given by 12x, 17x and 25x. According to the question,           Perimeter = 540 feet    Or,  12x + 17x + 25x = 540   .....

27. The population of a city 2 years ago was 40000. What is the present population of the city if the growth rate of the population is 2.5%. How much population has increased in 2 years?

Given,        Population of city 2 years ago (P) = 40000        Rate of population growth (R) = 2.5%       Time (T) = 2 years        Increase in population in 2 years (PT) .....

28. The population of a certain city is 250000. If the annual birth rate and death rate are 3.5% and 1.5% respectively, find the population of the city 3 years hence?

Given,      Population of a city (P) = 250000      Annual birth rate (Rb) = 3.5%      Annual death rate (Rd) = 1.5% So,      Annual growth rate (R) = Rb - Rd        .....

29. The population of a village increases every year by 5%. At the end of two years, the total population of the village will be 10,000 when 1025 will migrate to other places. What was the population of the village in the beginning?

Given,        Rate of population growth (R) = 5%        Population after two years (PT) = 10000        Out migration (O) = 1025 We know, Population after two years (PT) = P (1 + R100)T .....

30. The value of a machine costing Rs. 2400 is depreciated every year by 10%, what will be the value of the machine after one year?

Here,       Original value = Rs. 2400       Depreciated rate = 10%       Price after 1 year = ? We know, Value of machine after one year                 .....

31. A motor cycle which is supposed to depreciate at the rate of 5% per year was sold at Rs.57,000 after a year. At what price was it bought?

Here, Selling price of motor cycle after a year (PT ) = Rs. 57000 Time period (T) = 1 year Rate of depreciation (R) = 5% Initial price of the motor cycle (P) =? We have,       PT = P (1- R100)T Or, Rs. 57000 = P(1- 5100)1 Or, .....

32. The present population of a village is 30,000. If it is increased at the rate of 10% per annum, what will be the population after 2 years?

Given,        Present population (P) = 30000        Increase Rate (R) = 10%        Time period (T) = 2 years        Population after two years (P2) = ?  Now,   .....

33. Hari sold a bicycle costing Rs. 5500 after one year at Rs. 5060. At what percent was it depreciated?

Here, Initial cost of bicycle = Rs. 5500 Cost of bicycle after one year = Rs. 5060 So, Amount of depreciation = Rs. 5500 – Rs. 5060                               .....

34. If the cost is depreciated at the rate of 10% per annum, the cost of a motorcycle after 3 years becomes Rs. 92583. Calculate the original price of the motorcycle.

Here,       Cost of the motorcycle after 3 years(PT) = Rs.92583       Rate of depreciation (R) = 10%       Time (T) = 3 years        Original price of the motorcycle (P) = ? We know .....

35. The population of Ratnanagar was 40000 two years ago. If the population at present is 44100, find the population growth rate.

Given,        Original population (P) = 40000        Population after 2 years (PT) = 44100        Time period (T) = 2 years        Growth rate (R) = ? We have,   .....

36. The present population of a town is 40,000. If the population increases by 2% by birth and 3% by immigration, what will be the population of the town after 2 years?

Given,        Present population (P) = 40000        Increase rate by birth(R1) = 2%        Increase rate by immigration(R2) = 3%        Total increase rate (R) = 2% + 3% .....

37. Two years ago, the population of Jajarkot district was 120000 and now it is 122412. If crude death rate of the district was 5%, what was the crude birth rate of the district?

Here,        Present population (PT) = 122412        Previous population (P) = 120000        Crude death rate = 5% So, if the birth rate is x%.        .....

38. The value of a machine depreciates at the rate of 20% p.a. compound depreciation. Find the total compound depreciation after 3 years if the present value is Rs. 175000.

Here,      Present price (P) = Rs. 175000      Rate of depreciation(R) = 20%      Time (T) = 3 years We know that,  PT = P (1- R100)T       = 175000 (1- 20100)3     .....

39.

The population of Ramkot village increases every year by 2.5%. At the end of two years, the population of the village was 24895. If 320 people were migrated to the other village, what was the population of the village in the beginning?

Here,      Population at the end of two years = 24895      No. of people                                         .....

40. A sewing machine bought at Rs. 3200 depreciates at the rate of 5% per annum. Find its value at the end of two years. What is the amount of depreciation in 2 years?

Given,        Cost of the sewing machine (P) = Rs. 3200        Rate of depreciation (R) = 5%       Time (T) = 2 years We know, Value at the end of 2 years (DT) = P (1 - R100)T     .....

41. 3 years ago a district had population 375000 and the annual population growth rate 2%. If at the end of second year 1480 people were migrated in and 2750 people died due to the epidemic disease, find the present population of the district.

Here,      The population of the district 3 years ago (P) = 375000      The annual growth rate (R) = 2%      No. of people migrated at the end of second year = 1480      No. of people who .....

42. The value of a DVD player bought for Rs. 4000 some years ago was depreciating at the rate of ¼ of its value at the beginning of each year. If its present value is Rs. 2250, when was it bought?

Given,       Cost price of the DVD player (P) = Rs. 4000       Rate of depreciation (R) = ¼ of value at the beginning                         .....

43. Three electric fans were bought for Rs. 5250 in an auction 3 years ago. But the electric fans could not work properly so they are sold for Rs. 896 each at present. At what rate was it depreciated?

Given,       Cost price of the three fans (C) = Rs. 5250       Cost price of one fan (P) = Rs. 5250 / 3                                .....

44. A car was bought for Rs. 325000 two years ago. In two years, the owner of the car spent Rs. 6630 in repairing. If he sold the car now at 12% compound depreciation, find the profit or loss of the owner.

Given,       Cost price of the car two years ago (C) = Rs. 325000       Cost on repairing (R) = Rs. 6630       Time (T) = 2 years       Rate of depreciation (R) = 12%     .....

45. The electric items production industry declared to cut off its 10% workers every year due to the decreasing status of market. There are 40000 workers recently working in the company. Accordingly how many workers were there in the industry before 3 years? Find it?

Here,         The present number of the workers in the industry (P) = 40000         The number of the workers in the industry before 3 years (P3) = ?         The rate of cut off (R) = .....

46. A bus which was bought for Rs. 2400000 was sold at Rs. 2208000 in one year. At what percent was it depreciated?

Given,        Cost price of the bus (P) = Rs. 2400000        Selling price of the bus (DT) = Rs.2208000        Time (T) = 1 year        Rate of depreciation (R) = ? We .....

47. The population of a district two years ago was 62500. The present population of the district is 67600. At what rate was the population increased?

Given,        Population of city 2 years ago (P) = 62500        Present population of district (PT) = 67600        Time (T) = 2 years        Rate of growth (R) = ? We .....

48. In the beginning of 2065 B.S, the population of a town was 100000 and the rate of population growth is 2% every year. If in the beginning of 2066 B.S, 8000 people migrated to the place from different place. What will be the population in the beginning of 2068?

Here,      Rate = 2%,      Initial population = 100000 Now, Population in 2066, Population = P (1+  R100)T                    = 100000 (1+ 2100)1   .....

49. The population of a district 2 years ago was 64000 and the growth rate of the population was 2.5% per year. If at the end of second year the number of inhabitants leaving and entering the district are 1025 and 848 respectively and the number of deaths are 604, find the present population.

Given,       Population of the district 2 years ago (P) = 64000       Growth rate of population (R) = 2.5%       Number of inhabitants leaving the district (O) = 1025       Number of .....

50. The population of a village increases every year by 10%. At the end of two years, the total population of the village will be 30,000 when 5800 will be added by migration, what was the population of the village in the beginning?

Given,        Rate of population growth (R) = 10%        Time (T) = 2 years        Population after 2 years (PT) = 30000        In migration (I) = 5800     .....