Solve the problem.
-One leg of a right triangle is 21 inches longer than the other, and the hypotenuse is 24 inches longer than the shorter leg. Find the lengths of the three sides of the triangle.
A) 15 in., 36 in., 39 in.
B) 16 in., 37 in., 40 in.
C) 12 in., 33 in., 36 in.
D) 14 in., 35 in., 40 in.

Question

Quizplus · Accepted Answer

Using the Pythagorean theorem, $a^2 + b^2 = c^2$, where $a$ and $b$ are the legs and $c$ is the hypotenuse. Let $x$ be the length of the shorter leg. Then, the other leg is $x + 21$, and the hypotenuse is $x + 24$. Setting up the equation: $x^2 + (x + 21)^2 = (x + 24)^2$. Solving for $x$ gives $x = 15$, so the sides are 15 in., 36 in. (15+21), and 39 in. (15+24).

Solve the Problem. -One Leg of a Right Triangle Is 21 Inches Longer