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

Answer:

Check the similar triangle with sides #1#, #2#, #3# against Pythagoras formula to find that this is not a right angled triangle.

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 #a#, #b# and #c# by any non-zero number before applying the test.

In our example, all of the sides are divisible by #6# so let us assign:

#a = 6/6 = 1#

#b = 12/6 = 2#

#c = 18/6 = 3#

We find #a^2+b^2 = 1^2+2^2 = 1+4 = 5 != 9 = 3^2 = c^2#

In fact these side lengths only form a degenerate 'triangle' of zero area, with interior angles #0#, #0# and #pi#