Right Triangle?

Question

In a right triangle, the ratio of the hypotenuse to the shorter leg is 3 to 1. The length of the longer leg is 5'. Find the length of the shorter leg.

Answer 1

Let x be the length of the shorter leg.
Let 5 be the length of the longer leg.
Let 3x be the length of the hypotenuse.

Using the Pythagorean theorem:
5² + x² = (3x)²

Multiply out:
25 + x² = 9x²

Subtract x² from both sides:
25 = 8x²

Divide both sides by 8:
x² = 25/8

Take the sqrt of both sides:
x² = 50/16
x = 5 sqrt(2) / 4

x ≈ 1.76776695 ft.