SOLUTION: A piece of wire is 8 inches long. The wire is cut into two pieces and then each piece if bent into a square. Find the length of each piece if the sum of the areas of these squares

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: A piece of wire is 8 inches long. The wire is cut into two pieces and then each piece if bent into a square. Find the length of each piece if the sum of the areas of these squares       Log On


   

Question 536603: A piece of wire is 8 inches long. The wire is cut into two pieces and then each piece if bent into a square. Find the length of each piece if the sum of the areas of these squares is to be 2 square inches.
square 1: x/4 by x/4
square 2: 8-x/4 by 8-x/4
Answer by fcabanski(1391) About Me  (Show Source):
You can put this solution on YOUR website!
The combined area is the sum of the areas.


A=s%5E2 for each one.


Square 1: A=%28x%2F4%29%5E2


Square 2: A=%28%28x-8%29%2F4%29%5E2


Combined Area: A=2=%28x%2F4%29%5E2%2B%28%28x-8%29%2F4%29%5E2=


%28x%5E2%2F16%29%2B%28x%5E2-16x%2B64%29%2F16=2=


2x%5E2-16x%2B64=32 (Added the fractions on the left, then multiplied both sides by 16.)


Subtract 32 from each side.


x%5E2-16x%2B32=0


Factor with reverse FOIL. You may recognize the factors just by looking it.


%28x-4%29%28x-4%29


x-4=0 Add 4 to both sides. x=4.


The first piece is x and the second piece is 8-x.


X=4 so both pieces are 4 inches.

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