The shorter leg of a right triangle is 6cm shorter than the longer leg.

Question

The shorter leg of a right triangle is
6cm
shorter than the longer leg. The hypotenuse is
6cm
longer than the longer leg. Find the side lengths of the triangle.

Answer 1

Hi Kay,

 

This problem involves the Pythagorean theorem, and carefully defining your sides.

 

Let's call the long side x. The short side is 6 less than x. The hypotenuse is 6 more than x.

 

Long side: x

Short side: x - 6

Hypotenuse: x + 6

 

Pythagorean theorem:

(x)² + (x-6)² = (x+6)²

x² + x² - 12x + 36 = x² + 12x + 36   //the colored terms cancel, then subtract 12x from both sides.

x² - 24x = 0

x(x-24) = 0

x = 0 (impossible)

or

x = 24.

 

Long side = 24

Short side = 24-6 = 18

Hypotenuse = 24+6 = 30