Answer: The hypotenuse is 26 ft.
Step-by-step explanation: Let's call the shorter leg of the triangle x. The hypotenuse would be x + 16 and the other leg is y.
As the area is 120, we know that x.y/2 = 120 (because it's a right triangle).
This way, y = 240/x
we know that in a right triangle, we have a² = b² + c²
(x + 16)² = x² + y²
(x + 16)² = x² + (240/2)²
x² + 32x + 256 = x² + 57600/x²
32x + 256 = 57600/x²
32x³ + 256x² = 57600 (÷ 32)
x³ + 8x² = 1800
x = 10
∴
x + 16 = 26
y = 240/10 = 24
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