Question

The width of a rectangular fence is 5 feet less than the length. If the length is decreased by 3 feet and the width is increased by 1 feet , the area limited by the new fence will be the same as the area of the original fence.Find the dimensions of the original rectangular fence.

Answer 1

The length and width of the rectangular fence is 6 feet and 1 feet respectively.

Step-by-step explanation:

Let the length of the rectangular fence = L feet

Width of a rectangular fence is 5 feet less than the length.

Let width of a rectangular fence = W = (L - 5) feet

Area of the rectangular fence = L x W = L(L - 5) feet²

If length is decreased by 3 feet.

New length = L = L - 3 feet

New width is increased by 1 feet = W = (L - 5) + 1 = L - 4  feet

New area = L x W = (L - 3)(L - 4) feet²

The area limited by the new fence will be the same as the area of the original fence.

L(L - 5) = (L - 3)(L - 4)

=> L² - 5L = L² - 4L - 3L + 12

=> L² - 5L = L² - 7L + 12

=> 7L - 5L = 12

=> 2L = 12

=> L = $\frac{12}{2}$ = 6 feet

W = L - 5 = 6 - 5 = 1 feet

Hence, the length and width of the rectangular fence is 6 feet and 1 feet respectively.