# 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: 20, 6, 21?

Apr 18, 2017

The Pythagorean Theorem tells us that a triangle has a right angle if and only if the length of the longest side (the "hypotenuse") squared is equal to the some of the squares of the other two sides.

#### Explanation:

In this case, if the triangle were a right-angled triangle
${21}^{2}$ would need to be equal to ${6}^{2} + {20}^{2}$

Without doing the actual calculation we can see that
$\textcolor{w h i t e}{\text{XXX}} {21}^{2}$ is an odd number, and
$\textcolor{w h i t e}{\text{XXX}} {6}^{2} + {20}^{2}$ is an even number
so these values can not be equal (and the triangle does not contain a right angle)>

Apr 18, 2017

Pythagorean Theorem refers to right-angled triangles.

#### Explanation:

In a right angled triangle, the square of the hypotenuse is equal to
the sum of the squares of the other two sides.

${a}^{2} + {b}^{2} = {c}^{2}$

C will be the longest side of the triangle, in this case, 21

${20}^{2} + {6}^{2} = 436$

However, ${21}^{2} = 441$

Hence, it is not a right-angled triangle.