Question

A sqware has an area of 49 sqware feet. A rectangle has an area of 24 sqware feet its lanth is 2 feet longer than its width witch shape has the greater premeter

Answer 1

Explanation:

If the square has an area of 49 ft^2, then the length of one of its sides is

s = √(49 ft^2) = 7 ft, and its perimeter is P = 4(7 ft) = 28 ft.

As for the rectangle: let W and L represent the width and length, respectively. Then W*L = 24 ft^2 is the area. L = W + 2 ft. Therefore,

W(W + 2) = 24, or W^2 + 2W - 24 = 0, or (W +6)(W - 4) = 0. Thus, W = 4 ft.

The perimeter of this rectangle is P = 2W + 2L, or

P = 2(4 ft) + 2(6 ft) = 24 ft.

The square has the larger perimeter: It is 28 ft.