Question 885973: A piece of wire 60 inches is cut into two pieces and then each piece is bent into the shape of a square. If the sum of the areas of the two square is 117 square inches, find the length of each piece of wire.
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! A piece of wire 60 inches is cut into two pieces and then each piece is bent into the shape of a square.
If the sum of the areas of the two square is 117 square inches,
find the length of each piece of wire.
:
Let x = side of one square; let y = side of the other square
:
write an equation for each statement
"A piece of wire 60 inches is cut into two pieces"
4x + 4y = 60
simplify, divide by 4
x + y = 15
y = (15-x)
:
"the sum of the areas of the two square is 117 square inches"
x^2 + y^2 = 117
replace y with (15-x)
x^2 + (15-x)^2 = 117
FOIL (15-x)(15-x)
x^2 + 225 - 15x - 15x + x^2 = 117
combine like terms
2x^2 - 30x + 225 - 117 = 0
2x^2 - 30x + 108 = 0
simplify divide by 2
x^2 - 15x + 54 = 0
Factors to
x = 6
x = 9
therefore
4(6) = 24" is one piece of wire
and
4(9() = 36" is the other
:
:
Check this on calc: 6^2 + 9^2 = 117
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