# The diagonal of a rectangle measures 25cm. The width of the rectangle is 7cm. How do you find the length of the rectangle in cm?

Oct 14, 2015

The height (length) is $\text{24 cm}$.

#### Explanation:

The diagonal of a right triangle is the hypotenuse and is designated as side $c$. The width of a right triangle is side $b$, and the height is side $a$. You are looking for side $a$.

The Pythagorean equation is ${c}^{2} = {a}^{2} + {b}^{2}$.
$c = \text{25 cm}$
$b = \text{7 cm}$
a=?

Rearrange the equation to solve for side $a$.

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

Substitute the known values into the equation.

${a}^{2} = {\left(25 \text{cm")^2-(7"cm}\right)}^{2} =$

${a}^{2} = 625 {\text{cm"^2"-"49"cm}}^{2} =$

${a}^{2} = 576 {\text{cm}}^{2}$

Take the square root of both sides.

$\sqrt{{a}^{2}} = \sqrt{576 \text{cm"^2}}$

$a = \text{24 cm}$