# How do you find the hypotenuse of a right triangle with legs measuring 5.2 cm and 7.8 cm respectively?

##### 1 Answer
May 9, 2018

The length of the hypotenuse is $\text{9.4 cm}$.

#### Explanation:

Use the Pythagorean theorem:

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

where:

$c$ is the hypotenuse, and $a = \text{5.2 cm}$ and $b = \text{7.8 cm}$.

Plug the given values into the equation.

${c}^{2} = {\left(\text{5.2 cm")^2 + ("7.8 cm}\right)}^{2}$

Simplify.

${c}^{2} = \text{27.04 cm"^2"+ 60.84 cm"^2}$

Simplify.

${c}^{2} = \text{87.88 cm"^2}$

Take the square root of both sides.

$c = \sqrt{\text{87.88 cm"^2}}$

$c = \text{9.4 cm}$ (rounded to one decimal place)

The length of the hypotenuse is $\text{9.4 cm}$.