Question

The height of a parallelogram is one-third of its base. If the area of the parallelogram is 108 cm², find its base and height.

Answer 1

Let the base of the parallelogram be x cm.
Then, the height of the parallelogram will be $\frac{1}{3}$x cm.
It is given that the area of the parallelogram is 108 cm².

Area of a parallelogram = Base $\times$ Height
∴ 108 cm² = x $\times$ $\frac{1}{3}$x
108 cm² = $\frac{1}{3}$x²
⇒ x² = (108 $\times$ 3) cm² = 324 cm²
⇒ x² = (18 cm)²
⇒ x = 18 cm

∴ Base = x = 18 cm
Height = $\frac{1}{3}$x = $\left(\frac{1}{3}\times 18\right)$ cm
= 6 cm