SOLUTION: the sum of the perimeters of two square lots is 140 meters while the sum of their areas is 625 square meters. what are the measures of the side of the squares? i also need solution

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Question 680004: the sum of the perimeters of two square lots is 140 meters while the sum of their areas is 625 square meters. what are the measures of the side of the squares? i also need solutions
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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the sum of the perimeters of two square lots is 140 meters
while the sum of their areas is 625 square meters.
what are the measures of the side of the squares?
:
Let x = the side of one of the square lots
Let y = the side of the other
Perimeter sum
4x + 4y = 140
simplify, divide by 4
x + y = 35
y = (35-x)
:
The area sum
x^2 + y^2 = 625
replace y
x^2 + (35-x)^2 = 625
FOIL
x^2 + 1225 - 70x + x^2 = 625
2x^2 - 70x + 1225 - 625 = 0
2x^2 - 70x + 600 = 0
Simplify divide by 2
x^2 - 35x + 300 = 0
Factors to
(x-20)(2-15) = 0
Two solutions
x = 20, then y = 15
x = 15, then y = 20
:
The sides of the two squares are 15 and 20
:
Check this
4(20) + 4(15) = 140
20^2 + 15^2 = 625