Question

The length of a diagonal of a square is 18√2 inches. Find the perimeter of the square.

Answer 1

A diagonal of a square is defined, $d=a\sqrt{2}$ where a is side of the square. Solve for a to get $a=\frac{d}{\sqrt{2}}$.

Now multiply a by 4 since that is the definition of a perimeter,

$P=4a=4\cdot\frac{18\sqrt{2}}{\sqrt{2}}=4\cdot18=\boxed{72}$.

Hope this helps.