Solve.
-The longer leg of a right triangle is 14 inches longer than the other leg. Find the length of the two legs if the hypotenuse is 26 inches.
A) 10 in. and 24 in.
B) 8 in. and 22 in.
C) 9 in. and 23 in.
D) 11 in. and 25 in.

Question

Quizplus · Accepted Answer

Using the Pythagorean theorem, $a^2 + b^2 = c^2$, where $c$ is the hypotenuse and $a$ and $b$ are the legs of the triangle. Let $x$ be the length of the shorter leg; then the longer leg is $x + 14$. Substituting these into the theorem gives $x^2 + (x + 14)^2 = 26^2$. Solving this equation yields $x = 10$, so the legs are 10 inches and 24 inches long.

Solve. -The Longer Leg of a Right Triangle Is 14 Inches