Question

Find the area of a square whose diagonal is `12sqrt(12)"cm"`

Answer 1

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 = `12sqrt(2)"cm"`
Let the side of the square = s
∴ `sqrt("s"^2  + "s"^2) = 12sqrt(2)`
⇒ `sqrt(2"s"^2) = 12sqrt(2)`
⇒ `"s"sqrt(2) = 12sqrt(2)`
⇒ s = 12
We know, 
The area of a square with side s = s²
∴ s²
= (12)²
= 144cm².