Question

Estimate the side length of a square that has a 9 cm long diagonal. ( The perimeter of a square is typically 2.8 times bigger than the diagonal)

Answer 1

The diagonal and two adjacent sides of the square form an isosceles right triangle.

By the Pythagorean theorem

`\begin{gathered} s^2+s^2=9^2 \\ 2s^2=81 \\ s^2=(81)/(2) \\ s=\sqrt[]{(81)/(2)} \\ s=\frac{9}{\sqrt[]{2}} \\ s=6.36\text{ cm} \end{gathered}`