The shorter leg of a right triangle is 5 meters. The hypotenuse is 1meter longer than the longer leg. Find the length of the longer leg.

Question

Quizplus · Accepted Answer

Let x be the length of the longer leg. Then, by the Pythagorean theorem, $x^2 + 5^2 = (x+1)^2$. Expanding the right side gives $x^2 + 25 = x^2 + 2x + 1$. Simplifying this equation yields $2x = 24$, and thus $x = 12$. Therefore, the length of the longer leg is 12 meters, which corresponds to choice C.

The Shorter Leg of a Right Triangle Is 5 Meters