Question

A triangle has sides of lengths 10, 24, and 26. Is it a right triangle? Explain.

Answer 1

The most efficient way of finding the answer to this question is first reducing 10-24-26 and comparing it with the first 5 combinations for right-angled triangles:

First, reduce 10-24-26 by dividing it by the GCF (greatest common factor). 

10-24-26 divided by its GCF, 2, is:  5-12-13

Now comparing it with the first 5 combinations for right-angled triangles:

1)   3-4-5
2)  5-12-13
3)  7-24-25
4)  8-15-17
5)  20-21-29

As you can see, number 2 is the same as our reduced example. Therefore, we know that 10-24-26 is a right triangle. 

Hope this helps!