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?

Solution

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

diagonal of a rectangle = 12 cm

one of the sides of the rectangle = $$\frac{12}{2}$$ = 6 cm

$$\left(diagonal\right)^2\ =\ \left(one\ side\right)^2\ +\left(another\ side\right)^2\ $$

$$\left(12\right)^2\ =\ \left(6\right)^2\ +\left(another\ side\right)^2\ $$

$$144=\ 36\ +\left(another\ side\right)^2\ $$
$$144-36=\ \left(another\ side\right)^2\ $$
$$108=\ \left(another\ side\right)^2\ $$
$$\sqrt{108}=\ another\ side$$
$$6\sqrt{3}=\ another\ side$$
Area of this rectangle = product of both sides
= $$6\times\ 6\sqrt{3}$$
= $$36\sqrt{3}$$ cm$$^2$$