# What is the length, in units, of the hypotenuse of a right triangle if each of the two legs is 2 units?

Nov 25, 2016

The hypotenuse is $\sqrt{8}$ units or 2.828 units rounded to the nearest thousandth.

#### Explanation:

The formula for a the relationship between the sides of a right triangle is:

${a}^{2} + {b}^{2} = {c}^{2}$ where the $c$ is the hypotenuse and $a$ and $b$ are the legs of the triangle forming the right angle.

We are given $a$ and $b$ equal to 2 so we can substitute this into the formula and solve for $c$, the hypotenuse:

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

$4 + 4 = {c}^{2}$

$8 = {c}^{2}$

$\sqrt{8} = \sqrt{{c}^{2}}$

$c = \sqrt{8} = 2.828$