Solve the problem.
-A lot is in the shape of a right triangle. The shorter leg measures 90 meters. The hypotenuse is 30 meters longer than the length of the longer leg. How long is the longer leg?
A) 150 meters
B) 90 meters
C) 120 meters
D) 180 meters

Question

Quizplus · Accepted Answer

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). Let's denote the longer leg as x. According to the problem, the hypotenuse is 30 meters longer than the longer leg, so the hypotenuse is x + 30 meters. The equation based on the Pythagorean theorem is: $90^2 + x^2 = (x + 30)^2$. Simplifying this equation: $8100 + x^2 = x^2 + 60x + 900$. Subtracting $x^2$ from both sides and moving terms around gives: $7200 = 60x$, which simplifies to $x = 120$ meters.

Solve the Problem. -A Lot Is in the Shape of a Right Triangle