Question 1

A rectangular park has length and breadth in the ratio 3 : 2. A cyclist riding along its boundary at 12 km/hr takes 8 minutes to complete one round. Find the park's area in sq. m.

IUC Academy · Accepted Answer

153600 sq. m

Question 2

The width of a rectangular field is 60% of its length and its perimeter is 800 m. Find its area.

IUC Academy · Accepted Answer

37500 sq. m

Question 3

A rectangular farm has to be fenced on one long side, one short side and the diagonal. If the cost of fencing is ₹ 100 per m, the area of the farm is 1200 m2 and the short side is 30 m long, how much would the job cost?

IUC Academy · Accepted Answer

₹ 12000

Question 4

The perimeter of a rectangular field is 480 metres and the ratio between the length and the breadth is 5 : 3. The area is

IUC Academy · Accepted Answer

13500 sq. m — Let the length and breadth of the field be (5x) metres and (3x) metres respectively. Then, 2(5x + 3x) = 480 ⇒ 8x = 240 ⇒ x = 30. So, length = 150 m, breadth = 90 m. ∴ Area of the field = (150 × 90) sq. m = 13500 sq. m.

Question 5

A carpenter is designing a table. The table will be in the form of a rectangle whose length is 4 feet more than its width. How long should the table be if the carpenter wants the area of the table to be 45 sq ft?

IUC Academy · Accepted Answer

9 ft — Let the width of the table be x feet. Then, length of the table = (x + 4) ft. ∴ x(x + 4) = 45 ⇒ x2 + 4x – 45 = 0 ⇒ x2 + 9x – 5x – 45 = 0 ⇒ x(x + 9) – 5(x – 9) = 0 ⇒ (x + 9)(x – 5) = 0 ⇒ x = 5. Hence, length of the table = (5 + 4) ft = 9 ft.

Question 6

A rectangular plot is 20 m longer than it is wide. Fencing it at ₹ 26.50 per metre costs ₹ 5300. How long is the plot, in metres?

IUC Academy · Accepted Answer

None of these

Question 7

The area of a rectangle is 252 cm2 and its length and breadth are in the ratio of 9 : 7 respectively. What is its perimeter?

IUC Academy · Accepted Answer

64 cm — Let the length and breadth of the rectangle be (9x) cm and (7x) cm respectively. Then, 9x × 7x = 252 ⇒ 63 x2 = 252 ⇒ x2 = 4 ⇒ x = 2. So, length = 18 cm, breadth = 14 cm. ∴ Perimeter = 2 (18 + 14) cm = 64 cm.

Question 8

A man is walking in a rectangular field whose perimeter is 6 km. If the area of the rectangular field be 2 sq. km, then what is the difference between the length and breadth of the rectangle?

IUC Academy · Accepted Answer

1 km — Let the length and breadth of the field be l and b km respectively. Then, 2 (l + b) = 6 or l + b = 3 and lb = 2. (l – b)2 = (l + b)2 – 4 lb = 32 – 4 × 2 = 1 ⇒ (l – b) = 1 m

Question 9

The perimeter of a rectangle is 60 metres. If its length is twice its breadth, then its area is

IUC Academy · Accepted Answer

200 m2 — Let the breadth of the rectangle be x metres. Then, length of the rectangle = (2x) metres. 2(2x + x) = 60 ⇒ 6x = 60 ⇒ x = 10. So, length = 20 m, breadth = 10 m. ∴ Area = (20 × 10) m2 = 200 m2.

Question 10

The length of a rectangular plot is thrice its breadth. If the area of the rectangular plot is 7803 sq. metres, What is the breadth of the rectangular plot?

IUC Academy · Accepted Answer

51 m

Question 11

The total cost of flooring a room at ₹ 8.50 per square metre is ₹ 510. If the length of the room is 8 m, its breadth is

IUC Academy · Accepted Answer

7.5 m

Question 12

The difference between the length and breadth of a rectangle is 23 m. If its perimeter is 206 m, then its area is

IUC Academy · Accepted Answer

2520 m2 — We have : (l – b) = 23 and 2 (l + b) = 206 or (l + b) = 103. Solving the two equations, we get : l = 63 and b = 40. ∴ Area = (l × b) = (63 × 40) m2 = 2520 m2.

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