The length of one leg of a right triangle is twice the length of the second leg...

Question

The length of one leg of a right triangle is twice the length of the second leg. The hypotenuse is 15 meters. Find the length of the sides.

Answer 1

The three sides can be described as,

a = x

b = 2x

c = 15m

where x is the unknown length of the shorter side, represented by a. Meaning b is longer side that is twice as long as side a.

Using the Pythagorean theorem:

(15m)² = (x)² + (2x)²

225 = x² + 4x²

225 = 5x²

45 = x²

(45)^1/2 = x

3(5)^1/2 = x

We know a is the shorter side:

a = x

a = 3(5)^1/2

We know b is the longer side:

b = 2x

b = 2*3(5)^1/2

b = 6(5)^1/2