Question

If the length of the square is x, then find the length of the diagonal.​

Answer 1

The required length of the diagonal of the square with the length of its side as $xcm$ is $\sqrt{2}x cm$.

Pythagoras' theorem states that in any right-angled triangle the square of the hypotenuse is equal to the sum of the squares of its other two sides.

Any two adjacent sides of a square with its diagonal touching the ends of these two adjacent sides form a right-angled triangle.

Assume the length of the diagonal of the square$=dcm$

Apply Pythagoras theorem to find its length.

$d^{2} =x^{2} +x^{2} \\d^{2} =2x^{2}\\d=\sqrt{2} x cm$

The required length of the diagonal of the square is $\sqrt{2}x cm$.