SOLUTION: The sum of the perimeter of two squares is 64cm. and the sum of their areas is 130sq.cm. How long is a side of each square?

Question 644271: The sum of the perimeter of two squares is 64cm. and the sum of their areas is 130sq.cm. How long is a side of each square?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Let x = the side of one square
Let y = the side of the other square
:
The sum of the perimeter of two squares is 64cm.
4x + 4y = 64
simplify, divide by 4
x + y = 16
y = (16-x)
:
and the sum of their areas is 130sq.cm.
x^2 + y^2 = 130
replace y with (16-x)
x^2 + (16-x)^2 = 130
FOIL (16-x)(16-x)
x^2 + 256 - 32x + x^2 = 130
x^2 + x^2 - 32x + 256 - 130 = 0
2x^2 - 32x + 126 = 0
simplify, divide by 2
x^2 - 16x + 63 = 0
Factors to
(x-7)(x-9) = 0
Two solutions
x = 7, then y = 9
x = 9, then y = 7
:
The sides of the two squares are 7 & 9
:
:
Check: 7^2 + 9^2 = 130 and 4(7) + 4(9) = 64
How long is a side of each square?
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