# The diagonal of a square has length 6 sqrt2 ft. How do you find the length of the side of the square?

Jan 8, 2017

The length of the side of the square is $6 f t$.

#### Explanation:

Since the diagonal of a square is also the hypotenuse of a right angled triangle where two sides are equal, we can use the Pythagorean theorem to determine the length of the sides.

Consider the length of any side of the square as $x$. According to the theorem, the sum of the squares of the two sides forming the right angle is equal to the square of the hypotenuse. Hence:

${x}^{2} + {x}^{2} = {\left(6 \sqrt{2}\right)}^{2}$

$2 {x}^{2} = 36 \cdot 2$

Divide both sides by $2$.

${x}^{2} = \frac{36 \cdot 2}{2}$

${x}^{2} = \frac{36 \cdot \cancel{2}}{\cancel{2}}$

${x}^{2} = 36$

$x = 6$