SOLUTION: The diagonal of a square has the length of 8 sqrt 2. Find the length of a side of the triangle.

Question 53688: The diagonal of a square has the length of 8 sqrt 2. Find the length of a side of the triangle.
Found 2 solutions by stanbon, aaaaaaaa:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Draw the square and the diagonal.
Label the sides as "x" and the diagonal as 8sqrt2
EQUATION:
x^2 + x^2 = (8sqrt2)^2
2x^2 = 64(2)
x^2=64
x=8
Each side is 8
Cheers,
Stan H.
Answer by aaaaaaaa(138) (Show Source): You can put this solution on YOUR website!
By the pythagorean theorem, about the sides of a right triangle:
, where c is the hypotenuse.
If you ignore two sides of a square, the remaining two sides and the diagonal form a right triangle. Since both sides we consider are equal, and we know the length of the diagonal, let's modify our equation a bit:

Distribute the exponentiation and solve:

or
Since the length of the side of an square has to be positive, the sides of the square measure 8.
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