Asked by Kevin
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
Answers
Answered by
Henry
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.
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.
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