# The hypotenuse of a right triangle is 15 centimeters long. One leg is 9 cm long. How do you find the length of the other leg?

Mar 22, 2018

The other leg is $\text{12 cm}$ long.

#### Explanation:

Use the Pythagorean theorem:

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

where:

$c$ is the hypotenuse, and $a$ and $b$ are the other two sides (legs).

Let $a = \text{9 cm}$

Rearrange the equation to isolate ${b}^{2}$. Plug in the values for $a$ and $c$, and solve.

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

${b}^{2} = {\left(\text{15 cm")^2-("9 cm}\right)}^{2}$

Simplify.

${b}^{2} = \text{225 cm"^2-81 "cm"^2}$

${b}^{2} = \text{144 cm"^2}$

Take the square root of both sides.

$b = \sqrt{\text{144 cm"^2}}$

Simplify.

$b = \text{12 cm}$

Mar 22, 2018

$12$ centimeters long.

#### Explanation:

Since this is a right triangle, we can use the Pythagorean Theorem. $\text{c = hypotenuse}$
$\text{a = leg}$
$\text{b = leg}$

We can substitute in $c$ (the hypotenuse) and $a$ (one of the legs) to find the length of $b$ (the other leg)
${a}^{2} + {b}^{2} = {c}^{2}$
${9}^{2} + {b}^{2} = {15}^{2}$
$81 + {b}^{2} = 225$
${b}^{2} = 144$
$b = \sqrt{144}$
$b = 12$

So the other leg is $12$ centimeters long.