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Question 889432: a piece of wire 44 m long is cut into two parts and each part is bent to form a square. if the total area of two squares is 65cm^2.find the perimeter of two squares?
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! a piece of wire 44 m long is cut into two parts and each part is bent to form a square.
if the total area of two squares is 65cm^2,
:
Let x = the side of 1 square
Let y = the side of the other square
:
x^2 + y^2 = 65
and
4x + 4y = 44
Simplify, divide by 4
x + y = 11
y = (11-x)
:
In the area equation, replace y with (11-x)
x^2 + (11-x)^2 = 65
FOIL (11-x)(11-x)
x^2 + 121 - 22x + x^2 = 65
Arrange to form a quadratic equation
2x^2 - 22x + 121 - 65 = 0
2x^2 - 22x + 56 = 0
simplify, divide by 2
x^2 - 11x + 28 = 0
Factors to
(x-7)(x-4) = 0
x = 7, then y = 4
and
x = 4, then y = 7
"find the perimeter of two squares?"
4(4) = 16 m one square
4(7) = 28 m the other square
:
:
See if this checks out, find the total area: 4^2 + 7^2 = 65 sq/m
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