SOLUTION: If point Q lies on side AB of square ABCD such that QC=(sqrt of 10) units and QD=(sqrt of 13) units, what is the area of square ABCD?

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Question 1103129: If point Q lies on side AB of square ABCD such that QC=(sqrt of 10) units and QD=(sqrt of 13) units, what is the area of square ABCD?
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
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1.x%5E2%2B%28x-y%29%5E2=10
2.x%5E2%2By%5E2=13
From eq. 2,
x%5E2=13-y%5E2
x=sqrt%2813-y%5E2%29
Substituting into eq. 1,
13-y%5E2%2B%28sqrt%2813-y%29%5E2-y%29%5E2=10
13-y%5E2%2B%2813-y%5E2%29-2y%2Asqrt%2813-y%29%2By%5E2=10
26-y%5E2-2y%2Asqrt%2813-y%29=10
y%5E2-16=2y%2Asqrt%2813-y%29
%28y%5E2-16%29%5E2=4y%5E2%2813-y%29
y%5E4-32y%5E2%2B256=52y%5E2-4y%5E4
5y%5E4-84y%5E2%2B256=0
Substitute u=y%5E2
5u%5E2-84u%2B256=0
%28u-4%29%285u-64%29=0
Two solutions in u,
u-4=0
u=4
y%5E2=4
We're only interested in positive x and y values,
y=2
and
5u-64=0
5u=64
u=64%2F5
y%5E2=64%2F5
y=8%2Fsqrt%285%29
y=%288%2F5%29sqrt%285%29
You can use the first y to solve for x since you're really only looking for x.
This y will also give you an answer but not the correct answer since the value of x-y will be negative which is not allowed.
x%5E2%2By%5E2=13
x%5E2%2B4=13
x%5E2=9
x=3
So the area of the square is,
A=x%5E2
A=9