# How does the length of the hypotenuse relate to the length of the legs?

Jan 3, 2016

The relation is called the Pythagorean Theorem. In any right triangle, the following relation is true:

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

where $a$ and $b$ are the legs (shorter sides) of a right triangle and $c$ is the hypotenuse (the longest side, which is opposite the right angle).

For example, a triangle with sides $3 , 4$ and $5$ can be shown to be a right triangle.

The legs of the triangle are $3$ and $4$, so $a = 3$ and $b = 4$. The longest side of the triangle, $5$, is the hypotenuse, so $c = 5$.

${a}^{2} + {b}^{2} = {c}^{2}$
${3}^{2} + {4}^{2} = {5}^{2}$
$9 + 16 = 25$
$25 = 25$