# What is the length of the diagonal of a rectangle whose width is 90 cm and whose length is 200 cm?

Mar 29, 2018

The diagonal is $\text{219.317122 cm}$.

#### Explanation:

The diagonal of a rectangle makes a right triangle, with the diagonal (d) as the hypotenuse, and the length (l) and width (w) as the other two sides.

You can use the Pythagorean theorem to solve for the diagonal (hypotenuse).

${d}^{2} = {l}^{2} + {w}^{2}$

$d = \sqrt{{l}^{2} + {w}^{2}}$

$l = \text{200 cm}$ and $w = \text{90 cm}$

Plug in $l$ and $s$ into the formula and solve.

${d}^{2} = {\left(\text{200 cm")^2+("90 cm}\right)}^{2}$

${d}^{2} = \text{40000 cm"^2 + "8100 cm"^2}$

${d}^{2} = \text{48100 cm"^2}$

Take the square root of both sides.

$d = \sqrt{\text{40000 cm"^2 + "8100 cm"^2}}$

$d = \sqrt{\text{48100 cm"^2}}$

$d = \text{219.317122 cm}$