# In a right triangle, if a=3 and b=6, what is the value of c?

Feb 10, 2016

$c = \sqrt{45}$

#### Explanation:

When trying to find the area of a right triangle, we use the Pythagorean Theorem:

${\textcolor{red}{a}}^{2} + {\textcolor{b l u e}{b}}^{2} = {\textcolor{g r e e n}{c}}^{2}$

In this case we are given the values for $\textcolor{red}{a}$ and $\textcolor{b l u e}{b}$, so:

${\left(\textcolor{red}{3}\right)}^{2} + {\left(\textcolor{b l u e}{6}\right)}^{2} = {\textcolor{g r e e n}{c}}^{2}$

Which is equal to:

$\left(\textcolor{red}{9}\right) + \left(\textcolor{b l u e}{36}\right) = {\textcolor{g r e e n}{c}}^{2}$
$\textcolor{p u r p \le}{45} = {\textcolor{g r e e n}{c}}^{2}$
$\sqrt{\textcolor{p u r p \le}{45}} = \sqrt{{\textcolor{g r e e n}{c}}^{2}}$

So:

$\textcolor{g r e e n}{c} = \textcolor{g r e e n}{\sqrt{45} = 3 \sqrt{5}}$

• Note: The answer could also be a decimal or fraction. I chose to represent it in this way because it is the most exact. You could find either of the other answers by using a calculator.