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Sita Devi wants to make a rectangular pond on the road side for the purpose of providing drinking water for street animals. The area of the pond will be decreased by 3 square feet if its length is decreased by 2 ft. and breadth is increased by 1 ft. Its area will be increased by 4 square feet if the length is increased by 1 ft. and breadth remains the same. Find the dimensions of the pond.

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$7 \times 4 f t$

$9 \times 5 f t$

$8 \times 3 f t$

$7 \times 5 f t$

answer is A.

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Detailed Solution

Let length of rectangular pond = x

and breadth of rectangular pond = y

Area of rectangular pond = xy

According to question-

(x - 2)(y + 1) = (xy - 3)

xy + x - 2y -2 = xy -3

x - 2y = -1 —-(1)

(x + 1). y = (xy + 4)

xy + y = xy + 4

y = 4 —(2)

Putting value of y in (1)

x - 2(4) = -1

x - 8 = -1

x = 7

Length of rectangular pond = 7 ft.

Breadth of rectangular pond = 4 ft.

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