A wire is 264 ft in length is to be cut into two pieces, one to form a rectangle whose length is four less than twice the width, and the other to form a square whose side is equal to the sum of the width and the length of the rectangle. how long is the shorter piece of wire

Answer 1

Width = X Ft.
Length = (2x-4) Ft.

Square:
Each side = x + (2x-4).

2x+2(2x-4) + 4(x + 2x-4) = 264 Ft.
2x+4x-8 + 4x+8x-16 = 264.
18x - 24 = 264.
18x = 288.
X = 16 Ft.

Rectangle = 2*16 + 2(2*16-4) = 88 Ft.

Square = 4(16+32-4) = 176 Ft.

So the shorter piece of wire = 88 Ft.