# A triangle has sides with lengths of 6 feet, 8 feet, and 10 feet. Is it a right triangle?

Nov 30, 2016

Yes, it is.

#### Explanation:

For a triangle to be right-angled, the Pythagorean Theorem has to apply, that is, the sum of the squares of two sides must equal the square of the third side (which would be the hypotenuse, the side facing the right angle).

If we square all the given sides we get the following:

${6}^{2} = 36$

${8}^{2} = 64$

${10}^{2} = 100$

It can easily be seen that the sum of $36$ and $64$ is $100$, hence:

${6}^{2} + {8}^{2} = {10}^{2}$ proves the Pythagorean theorem and the triangle is right-angled with the sides measuring $6 f t$ and $8 f t$ forming the right angle and the side measuring $10 f t$ being the hypotenuse.