# The perimeter of a square is 20 cm. How do you find the length of a diagonal?

Let $a$ be the side of the square .Its perimeter equals with $4 a$ hence $4 a = 20 \implies a = 5 c m$ .Now the diagonal $d$ is the hypotenese of the right triangle with sides those of the square so
${d}^{2} = {a}^{2} + {a}^{2} \implies d = \sqrt{2} \cdot a \implies d = 5 \cdot \sqrt{2}$