Question

The base of a parallelogram is twice its height. If the area of the parallelogram is 512 cm², find the base and height.

Answer 1

Let the height of the parallelogram be x cm.
Then the base of the parallelogram is 2x cm.
It is given that the area of the parallelogram = 512 cm²
So,
Area of a parallelogram = Base x Height
512 cm² = 2x x x
512 cm² = 2x²
⇒ x² = $\frac{512{\mathrm{cm}}^2}{2}=256{\mathrm{cm}}^2$
⇒ x² = (16 cm)²
⇒ x = 16 cm
Hence, base = 2x = 2 x 16 = 32 cm and height = x = 16 cm.