Solve.
-One leg of a right triangle is 35 inches longer than the smaller leg, and the hypotenuse is 40 inches longer than the smaller leg. Find the lengths of the sides of the triangle.
A) 25 in., 60 in., 65 in.
B) 20 in., 55 in., 60 in
C) 26 in., 61 in., 66 in
D) 24 in., 59 in., 66 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 smaller leg. Then, the other leg is $x + 35$ inches, and the hypotenuse is $x + 40$ inches. Setting up the equation: $x^2 + (x + 35)^2 = (x + 40)^2$. Solving this equation gives $x = 25$ inches. Therefore, the sides are 25 inches, 60 inches (25 + 35), and 65 inches (25 + 40), which matches option A.

Solve. -One Leg of a Right Triangle Is 35 Inches Longer