If the length of the diagonal of a square is 12 √2 cm, what is its perimeter?

The correct answer is: Perimeter of the given square is 48 cm.

Step-by-step solution:-
In the adjacent diagram, we can see that the diagonal divides the given square into 2 right angled triangles.
Also, diagonal of the square becomes the hypotenuse of the 2 triangles.
Hypotenuse of the given triangles = diagonal of the given square = 12 √2 cm
Let the sides of the given square be x cm.
∴ side of the triangles (other than hypotenuse) = x cm.
By applying Pythagorean theorem, For a right angled triangle-
Hypotenuse2 = sum of the squares of the remaining 2 sides
∴ (12√2)2 = x2 + x2
∴ 144 × 2 = 2x2
∴ 288 = 2x2
i.e. 2x2 = 288
∴ x2 = 288 / 2
∴ x2 = 144
∴ x = 12 .............................. (Taking square root both the sides) ........................ (Equation i)
Perimeter of the given square = 4 × side
∴ Perimeter of the given square = 4 × x
∴ Perimeter of the given square = 4 × 12 ...................................................................................... (From Equation i)
∴ Perimeter of the given square = 48 cm
Final Answer:-
∴ Perimeter of the given square is 48 cm.