Question

Which of the following sets of numbers could not represent the three sides of a right triangle?

13,84,85
33,44,55
3,4,5
15,20,24

Answer 1

Answer:

Step-by-step explanation:

The inverse of the Pythagorean Theorem says that if the hypotenuse squared is equal to the sum of the squares of the legs, you have a right triangle.  Do that with each one.  I'll do it for the first 2 to show you how they do work out to satisfy a right triangle and then do it for the one that doesn't so you can see how to use the theorem.  Use the formula for Pythagorean's Theorem and the fact that the hypotenuse is always the longest side of a right triangle.

$85^2=13^2+84^2$ so

$7225=169+7056$ and

7225 = 7225

So this is a right triangle.  Next one:

$55^2=33^2+44^2$ and

3025 = 1089 + 1936 and

3025 = 3025

So this is a right triangle too.

For the last set of numbers:

$24^2=15^2+20^2$ and

576 = 225 + 400 and

576 = 625

As you can see, those are not the same numbers so that is the choice that is NOT a right triangle.