SOLUTION: show a complete solution find the exact length of the side of a square whose diagonal is 3 ft. not sure how to set this up please help with step by step

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Question 81578: show a complete solution
find the exact length of the side of a square whose diagonal is 3 ft. not sure how to set this up please help with step by step
Answer by tutorcecilia(2152) About Me  (Show Source):
You can put this solution on YOUR website!
If the rectangle is a square, than all of the sides (x) are equal. Since the triangles formed are right triangles and the hypotenuse is the diagonal, use the Pythagorean Theorem to solve:
a^2+b^2=c^2
.
a=one side=x
b=another side=x
c=the hypotenuse=3
.
Plug-in the values and solve for the x-term
x^2+x^2=3^2
2x^2=9
2x^2/2=9/2
x^2=9/2
%28sqrt%28x%5E2%29%29=%28sqrt%289%2F2%29%29
x=%283%2Fsqrt%282%29%29
x=%283%28sqrt%282%29%29%2Fsqrt%282%29sqrt%282%29%29 [rationalize the denominator]
x=%283%28sqrt%282%29%29%2F2%29%29
.
check by plugging all of the values back into:
a^2+b^2=c^2
%283%28sqrt%282%29%29%2F2%29%5E2%29+%283%28sqrt%282%29%29%2F2%29%5E2%29=3^2