# What is the length of a diagonal of a rectangle with length 12 and width 5?

Nov 28, 2016

The length of the diagonal is 13.

#### Explanation:

The diagonal of a rectangle creates a right triangle with the length and width of the rectangle being the sides and the diagonal being the hypotenuse.

The Pythagoras theory states:

${a}^{2} + {b}^{2} = {c}^{2}$ for right triangles where $x$ is the hypotenuse.

We are given the length and width as 12 and 5 so we can substitute and solve for $c$:

${12}^{2} + {5}^{2} = {c}^{2}$

$144 + 25 = {c}^{2}$

$169 = {c}^{2}$

$\sqrt{169} = \sqrt{{c}^{2}}$

$13 = c$