# The legs of a right triangle measure 2sqrt3 and 5. What is the length of the hypotenuse?

May 7, 2016

$\sqrt{37}$

#### Explanation:

Pythagoras theorem gives us the equation:

${a}^{2} + {b}^{2} = {c}^{2}$ where $c$ is the hypotenuse and $a , b$ are the two legs.

Substitute the value of the two legs in.

${\left(2 \sqrt{3}\right)}^{2} + {5}^{2} = {c}^{2}$

$12 + 25 = {c}^{2}$

${c}^{2} = 37$

$c = \sqrt{37}$

Normally, when you take the square root of a square the answer should be $\pm$. However, a length can't be a negative, so $\sqrt{37}$ is the only solution.