Question

The height of a parellelogram is one third of it base if the area of parallelogram is 108cm power2 . Find it base and height

Answer 1

Let the base of the parallelogram be x cm.
Then, the height of the parallelogram will be 13x cm.
It is given that the area of the parallelogram is 108 cm2.

Area of a parallelogram = Base × Height
∴ 108 cm2 = x × 13x
108 cm2 = 13x2
⇒ x2 = (108 × 3) cm2 = 324 cm2
⇒ x2 = (18 cm)2
⇒ x = 18 cm

∴ Base = x = 18 cm
Height = 13x = (13×18) cm
= 6 cm

Answer 2

$\underline{\underline{\bold{Answer:}}}$

$\text{Base = 18 cm and height = 6 cm}$

$\underline{\underline{\bold{Complete\:Method:}}}$

Let the base of the parallelogram be x cm

Then, the height of the parallelogram be $\frac{\text{x}}{3}$ cm

It is given that the area of the parallelogram is 108 cm²

Now, area of the parallelogram = base × height

⇒ 108 = x * $\frac{\text{x}}{3}$

⇒ 108 * 3 = x²

⇒ x² = 324

⇒ x² = 18²

⇒ x = ± 18

∵ length cannot be negative, the value of x be 18

∴ base = 18 cm and
height = $\frac{18}{3}$ cm = 6 cm