The area of a square is 144 cm$^2$. What is the perimeter of the square formed with the diagonal of the original square as its side?

$48\sqrt{2}$ cm

We know ,

Area of square = ( Side )²

144 = ( Side )²

Side = 12

Diagonal of square = √2 × Side  = √2 × 12 = 12√2 cm

Side of new square = Diagonal of old square

Side of new square = 12√2  

Perimeter of new square = 4 × Side of new square 

= 4 × 12√2

= 48√2 cm