Question

given that the length of the diagonals of a square are 6 m each, find the length of its sides.

Answer 1

when the side is a m
by Pythagoras' theorem,
diagonal, d² = a² +a²
                   = 2a²
⇒d = a√2
now, diagonal =6 = a√2
⇒a= 6/√2 = 3√2
side length = 3√2 m

Answer 2

Let the sides of a square be `x`m
Given d = 6 m
We know that x² + x² = d²
⇒2x² = 6²
⇒2x² = 36
⇒ x² = 36/2
⇒ x² = 18
⇒ x = √18
⇒x = √9×2
∴ x = 3√2
∴Side of the square = 3√2 m