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?
Answer & explanation
Correct answer: option 3
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