SOLUTION: The perimeter of one square exceeds that of another by 16 and its area is 44 less than 4 times the area of the other. What is the length of the side of each side of each square?

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Question 164604: The perimeter of one square exceeds that of another by 16 and its area is 44 less than 4 times the area of the other. What is the length of the side of each side of each square?
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Let call the first square side a and the second square side b.
The perimeters are,
P%5Ba%5D=4a
P%5Bb%5D=4b
and the areas are,
A%5Ba%5D=a%5E2
A%5Bb%5D=b%5E2
.
.
.
"perimeter of one square exceeds that of another by 16"
P%5Ba%5D=P%5Bb%5D%2B16
1.4a=4b%2B16
its area is 44 less than 4 times the area of the other
A%5Ba%5D=4A%5Bb%5D-44
2.a%5E2=4b%5E2-44
Use eq. 1 to come up with an expression for a in terms of b.
1.4a=4b%2B16
a=b%2B4
Now substitute that expression for a in eq. 2 and solve for b.
2.a%5E2=4b%5E2-44
%28b%2B4%29%5E2=4b%5E2-44
b%5E2%2B8b%2B16=4b%5E2-44
3b%5E2-8b-60=0
%283b%2B10%29%28b-6%29=0
We'll only solve for the positive b solution since a negative length doesn't make sense.
b-6=0
highlight%28b=6%29
From eq. 1,
a=b%2B4
a=6%2B4
highlight%28a=10%29
.
.
.
P%5Ba%5D=4a=40
P%5Bb%5D=4b=24
A%5Ba%5D=a%5E2=100
A%5Bb%5D=b%5E2=36