9514 1404 393
Answer:
x = 25√2
Explanation:
The Pythagorean theorem is used to relate the sides of a right triangle to the hypotenuse. The sides are marked as being the same length, so both are x. Then we have ...
50² = x² + x²
50² = 2x² . . . . . . . . collect terms
2·(2500/4) = x² . . . . . multiply by 2/4*
√(2·625) = x . . . take the square root
25√2 = x
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* We use a version of 1/2 that has a prefect square in the denominator (2/4) so that we don't end up with an irrational denominator when we take the square root. It's a little bit of planning ahead.