Question

find the diagonal of a square whose side is 10 cm

Answer 1

The diagonal divides the square into 2 right angled triangles. now applying pythagoras theorem:
10^2 + 10^2 = 100+100=root over 200 = 10 root 2 cm

Answer 2

Answer:

=> $10\sqrt{2}$ cm

Step-by-step explanation:

Given that:-

The side of the square is $10$ cm,

To find:- The diagonal of a square,

In right angled, △ABC

By using the Pythagoras theorem

$AB^2+BC^2=AC^2$

As we know that, in square their sides are equal.

$=> AB= BC$

$=> 10^2+10^2=AC^2$

$=>100+100=AC^2$

$=>200=AC^2$

Taking square on both sides we get,

$=> AC=\sqrt{200}$

$=>AC=\sqrt{2\times 2\times 2\times 5\times 5}$

$=> AC=2\times 5\sqrt{2}$

$=> AC = 10\sqrt{2}cm$

Hence, the diagonal of a square is $10\sqrt{2}$ cm.