Find the area of a rectangle whose length is one-half of the perimeter, whose width is one fourth of the length, and whose perimeter is 60 inches.

Answer 1

It is not possible for the length of a rectangle to be 1/2 the perimeter, by definition. The equation for a perimeter of a rectangle is 2*width +2 * length = perimeter. If the length is 1/2 the perimeter, to solve this equation the width of the rectangle must be 0 which would not be a rectangle itself.

However if we find the area of a rectangle whose width is one fourth the length and the perimeter is 60 inches, we can do that:

w = 1/4 * L

2w + 2L = p, where w is width, L is length, and p is perimeter

Plugging in w = 1/4 * L:

2*1/4 L + 2L = p

5/2 L = p

L = p * 2/5

Since p = 60:

L = 60* 2/5 = 24

w = 1/4 * 24 =6

Area of this rectangle = 6 * 24 = 144 in^2