# A square has a perimeter of 12 centimeters. How do you find the length of the diagonal of the square?

Mar 7, 2016

The perimeter of a square is found by the formula $P = 4 c$

#### Explanation:

$P = 4 c$

$12 = 4 c$

$3 = c$

Since all the sides in a square are equal in length, the diagonals are equal in length. By Pythagoras Theorem we can find the length of one of the diagonals.

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

${3}^{2} + {3}^{2} = {c}^{2}$

$9 + 9 = {c}^{2}$

$18 = {c}^{2}$

$\sqrt{18} = c$

$3 \sqrt{2} = c$

The diagonal measures $3 \sqrt{2}$ cm.

Practice exercises:

1. A square has an area of 64 square meters. Find the perimeter of the triangle that is formed between two the sides and one of the diagonals.

2 . A rectangle has a perimeter of 24 cm. The length measures 7 cm. Find the distance between the two corners of the rectangle (the length of a diagonal)

Challenge Problem:

An isosceles triangle has lengths of $x - 2$, $x - 2$ and $2 x + 1$. Its perimeter is 41. Find the height of the triangle.

Good luck!