# How do you use the Pythagorean Theorem to determine if the following three numbers could represent the measures of the sides of a right triangle: 6, 8, 10?

Mar 14, 2016

As the left hand side value of the equation is the same as the value of the right hand side, the given numbers are the sides of a right triangle

#### Explanation:

Consider the general construction of a right triangle:

The Hypotenuse has to be longer than the other two sides otherwise you could not construct the triangle.

Thus, from the numbers in your list the Hypotenuse would have to be of length 10

So if these numbers are correct it would be true that

$\text{ } {10}^{2} = {6}^{2} + {8}^{2}$

Consider the right hand side:

${6}^{2} + {8}^{2} = 36 + 64 = 100$

As the left hand side value of the equation is the same as the value of the right hand side, the given numbers are the sides of a right triangle