The diagonal of a rectangle is 12 cm long, and it is twice as long as one of the sides of the rectangle. What is the area of this rectangle?

$36 \sqrt{3}$ cm²

We know that,

Area of a rectangle = Length × Breadth

Diagonal of a rectangle = \(\sqrt { Length^2 +  Breadth ^2}\)

Length of diagonal = 12cm

Then the side of a rectangle according to the question = \(\frac{12}{2}\)  = 6cm

So,

\(\sqrt { 6^2 +  Breadth ^2}\) = 12

= Breadth² + 36 = 144

= Breadth² = 108

= Breadth = 6\(\sqrt {3}\)

The area of the rectangle = 6\(\sqrt {3}\) × 6 = 36\(\sqrt {3}\) cm²