Question

The length of a diagonals of square is $\sqrt{2}(6+2\sqrt{5})cm$. Then finds the length of sides of the square.

Answer 1

As we know that,

Length of diagonal of a square $=\sqrt{2}a.....\left(1\right)$

Whereas $a$ is the side length of the square

Length of diagonal of square $=\sqrt{2}(6+2\sqrt{5})cm.....\left(2\right)\left(\text{Given}\right)$

Comparing equation $\left(1\right)\&\left(2\right)$, we get

$a=(6+2\sqrt{5})cm$

Hence lagth of side of given square is $(6+2\sqrt{5})cm$.