Solve.
-Find the length of the shorter leg of a right triangle if the longer leg is 24 meters and the hypotenuse is 6 more than twice the shorter leg.
A)17 m
B)10 m
C)18 m
D)9 m

Question

Quizplus · Accepted Answer

Let's call the shorter leg x.

According to the problem, we know:

- The longer leg = 24 
- The hypotenuse = 6 + 2x

We can use the Pythagorean theorem to create an equation:

x^2 + 24^2 = (6 + 2x)^2

Simplifying:

x^2 + 576 = 4x^2 + 24x + 36

3x^2 - 24x - 540 = 0

Dividing both sides by 3:

x^2 - 8x - 180 = 0

Factoring:

(x - 18)(x + 10) = 0

So x can be either 18 or -10. Since we're asked for the shorter leg, the answer is the positive value, x = 10.

Solve. -Find the Length of the Shorter Leg of a Right