# How do you find the length of their hypotenuses given sides 10 and 12?

Nov 6, 2015

The hypotenuse is $c = \sqrt{244}$.

#### Explanation:

For this, you use the Pythagorean Theorem. This theorem is ${a}^{2} + {b}^{2} = {c}^{2}$.

In any right triangle, you have 2 legs and a hypotenuse. The two legs are the shortest sides, and the ones that share the right angle, and the hypotenuse is the other side, and the longest side. The two legs are known as $a$ and $b$ and the hypotenuse is $c$.

Start off by plugging your sides (the legs in the case) into the formula. ${a}^{2} + {b}^{2} = {c}^{2} \implies {10}^{2} + {12}^{2} = {c}^{2}$. When you do the exponents, you get $100 + 144 = {c}^{2}$, and you can simplify to $244 = {c}^{2}$.

Now to reverse the exponent on the $c$, you must do the square root, to both sides. This is $\sqrt{244} = \sqrt{{c}^{2}}$. Since the square root of 244 is not rational, we leave our answer as $\sqrt{244}$.

So the hypotenuse is $c = \sqrt{244}$.