Question

The height of a parallelogram is one third of its base. If the area of the parallelogram is 192 cm², find its height and base.​

Answer 1

Step-by-step explanation:

Given

Area of parallelogram = 192cm2

The height of a parallelogram is one-third of its base

So

Let the base be x cm.

Height = 1/3x cm.

Area of Parallelogram = Base X Height

Base × Height = 192

x × 1/3x = 192

= 1/3 x2 = 192

= x2 = 192 × 3

= x2 = 576

x = √576

x = 24cm

Base = x = 24cm.

And Height = 1/3x = 1/3 × 24

= Height = 8 cm

Base= 24cm and height = 8cm

Answer 2

• Height of the parallelogram = 8 cm.
• Base of the parallelogram = 24 cm.

Given :–

• Area of the parallelogram = 192 cm²
• Height of the parallelogram is one third of its base.

To Find :–

• Height of the parallelogram.
• Base of the parallelogram.

Solution :–

Let,

• The height of the parallelogram be x.

• The base of the parallelogram be y.

According to the question,

Height of the parallelogram is one third of its base.

$\longmapsto x = \dfrac{1}{3} y$ –––(1)

We know that,

Area of the parallelogram = Base × Height

Base × Height = 192 cm²

$\longmapsto y \times \dfrac{1}{3} y = 192 \: {cm}^{2}$

$\longmapsto {y}^{2} = 192 \times 3 \: {cm}^{2}$

$\longmapsto {y}^{2} = 576 \: {cm}^{2}$

$\longmapsto y = \sqrt{576 \: {cm}^{2}}$

$\longmapsto y = 24 \: cm$

So,

• y = base = 24 cm.

Now, we have to find the height of the parallelogram.

Given that,

Height = $\dfrac{1}{3} y$

Now, substitute the value of base in eqn. (1),

$\longmapsto x = \dfrac{1}{\cancel3} \times \cancel{24} \: cm$

$\longmapsto x = {1} \times 8 \: cm$

$\longmapsto x = 8 \: cm$

Hence,

The height of the parallelogram (x) is 8 cm.

The base of the parallelogram (y) is 24 cm.

Check :–

Area of the parallelogram = Base × Height

Base × Height = 192 cm²

• Base = 24 cm.
• Height = 8 cm.

$\longmapsto 24 \: cm \times 8 \: cm = 192 \: {192 \: cm}^{2}$

$\longmapsto 192 \: {cm}^{2} = 192 \: {cm}^{2}$

Since, the area of the parallelogram 192 cm is equal to the given value of the area.

So, the base and the height of the parallelogram is 24 cm and 8 cm is correct.