The given figure requires we use the Pythagorean theorem to write two relations involving right triangle side lengths. The Pythagorean theorem tells us the square of the hypotenuse is the sum of the squares of the other two sides.
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<h3>Triangle EGH:</h3>
EG² = GH² +HE²
GH² = EG² -HE² = 53² -28² = 2025 . . . . . solve for GH², use given values
<h3>Triangle FGH:</h3>
FG² = GH² +FH²
FH² = FG² -GH² = 117² -2025 = 11664 . . . . solve for FH², use known values
