# A square has diaonal of 24cm what is the lenght of its sides?. pls help me quick homework due tommorow

Mar 21, 2018

The side length is $12 \sqrt{2}$ cm

#### Explanation:

If a square is divided into two triangles by its diagonal, it will form 2 special right triangles. These right triangles will have the angle measures 45 degrees, 45 degrees, and 90 degrees. The diagonal of the square will be the hypotenuse for each of these isosceles right triangles and the side lengths of the square will be the legs.

In 45-45-90 special right triangles, the ratio of the sides (leg:leg:hypotenuse) is $1 : 1 : \sqrt{2}$. That means the hypotenuse is the length of the legs multiplied by $\sqrt{2}$.

In this scenario, to find the length of each leg, divide the hypotenuse (24) by $\sqrt{2}$

$\frac{24}{\sqrt{2}} \rightarrow$ Rationalize the denominator

$\frac{24 \sqrt{2}}{2} \rightarrow$ Simplify by dividing the numerator by 2 (the denominator)

$12 \sqrt{2} \rightarrow$ Length of each side

Mar 21, 2018

$p = 16.971 c m$

#### Explanation:

diagonal
$d = 24 c m$

side be p

By pythagoras theorem

${p}^{2} + {p}^{2} = {d}^{2}$

${p}^{2} + {p}^{2} = {24}^{2}$

$2 {p}^{2} = {24}^{2}$

${p}^{2} = {24}^{2} / 2$

$p = \frac{24}{\sqrt{2}}$

$p = 16.971 c m$