Find the area of a square whose diagonal is 12 12 cm - Vidyadip

Question

Find the area of a square whose diagonal is $12 \sqrt{12} \ cm$

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Answer

The sides and diagonal of a square form a right triangle as each angle of a square is a right angle.
Diagonal is the side opposite to the right angle,
$\therefore$ it is the hypotenuse
Here, Diagonal of the square $=12 \sqrt{2} \ cm$
Let the side of the square $=s$
$ \therefore \sqrt{ s ^2+ s ^2}=12 \sqrt{2}$
$\Rightarrow \sqrt{2 s ^2}=12 \sqrt{2}$
$\Rightarrow s \sqrt{2}=12 \sqrt{2}$
$\Rightarrow s =12 $
We know,
The area of a square with side $s=s^2$
$ \therefore s ^2$
$=(12)^2$
$=144 \ cm ^2 . $

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