Question

A rectangular yard has an area of 96 square feet. if the width of the yard is 4 feet less than the length, what is the perimeter, in feet, of the yard?

Answer 1

40 ft

Explanation:

Let x represent the average of the length and width. Then the length is (x+2) and the width is (x-2). The area is the product of these:

96 = (x +2)(x -2) = x² -4

100 = x² . . . . . . add 4

10 = x . . . . . . . . square root

Since x is the average of two numbers, their sum is 2x. The perimeter of the yard is twice the sum of length and width, so is 4x = 4·10 = 40.

The perimeter of the yard is 40 feet.

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In case you care, the size of the yard is 8 ft by 12 ft.