Question

A large right triangle is going to be a part of a geometric sculpture, as shown below.

The hypotenuse will be 10 feet long. The length of one leg of the triangle is 4 feet less
than twice the other leg. Find the length of each leg, in feet, and separate them with a
comma.
H
ft
10
2x-4

Answer 1

Explanation:

Let's call one leg of the triangle "x" and the other leg "2x-4". We can use the Pythagorean theorem to solve for the lengths of the legs:

x^2 + (2x-4)^2 = 10^2

x^2 + 4x^2 - 16x + 16 = 100

5x^2 - 16x - 84 = 0

We can solve this quadratic equation by factoring or using the quadratic formula. Factoring gives us:

(5x + 14)(x - 6) = 0

So x = -14/5 or x = 6. We can discard the negative solution since we're dealing with lengths. Therefore:

x = 6

2x - 4 = 8

The lengths of the legs are 6 feet and 8 feet.