# How do you use the Pythagorean Theorem to determine if the three numbers could be the measures of the sides of a right triangle: 6, 12, 18?

##### 1 Answer

Feb 29, 2016

Check the similar triangle with sides

#### Explanation:

Three positive numbers can be the measures of the sides of a right triangle if and only if taken in ascending order they satisfy:

#a^2+b^2=c^2#

Also a triangle is a right triangle if and only if any similar triangle is a right triangle. So you can multiply or divide

In our example, all of the sides are divisible by

#a = 6/6 = 1#

#b = 12/6 = 2#

#c = 18/6 = 3#

We find

In fact these side lengths only form a degenerate 'triangle' of zero area, with interior angles