Question

base of a parallelogram is thrice of its height . if the area is 897 sq . cm . find the height and base of parallelogram .

Answer 1

Question:-

base of a parallelogram is thrice of its height . if the area is 897 sq . cm . find the height and base of parallelogram .

Answer:-

• The height and base of parallelogram are 17.29 cm and 51.87 cm

To find:-

• Height and base of parallelogram

Solution:-

• Area of parallelogram = 897 cm²

Let,

• Height of parallelogram = x
• Base of parallelogram = 3x

As we know,

$\large{ \boxed{ \mathfrak{area = b \times h}}}$

Where,

• b = base of parallelogram
• h = height of parallelogram

According to question,

$\large{ \rm : \implies \: \: \: \: \: \: \: \: \: x \times 3x = 897}$

$\large{ \rm : \implies \: \: \: \: \: \: \: \: \: 3 {x}^{2} = 897}$

$\large{ \rm : \implies \: \: \: \: \: \: \: \: \: {x }^{2} = \frac{897}{3} }$

$\large{ \rm : \implies \: \: \: \: \: \: \: \: \: {x}^{2} = 299}$

$\large{ \rm : \implies \: \: \: \: \: \: \: \: \: x = \sqrt{299} }$

$\large{ \rm : \implies \: \: \: \: \: \: \: \: \: x = 17.29}$

Now,

• Height = 17.29 cm
• Base = 51.87 cm

Hence,

The height and base of parallelogram are 17.29 cm and 51.87 cm

Answer 2

Given:

• Area of parallelogram = 897 sq. cm

To Find:

• Height of parallelogram
• Base of parallelogram

Solution:

Let,

• Height of parallelogram be x
• Base of parallelogram be 3 x

★Area of parallelogram:- Base × Height

Where,

• Area of parallelogram = 897 sq. cm
• Base = 3x
• Height = x

So,

→ x + 3x = 897

→ 3x² = 897

→ x² = 897/3

→ x² = 299

→ x = √299

→ x = 17.29

_____________________

Then,

★ Value of 3x.

→ 3(17.29)

→ 3 × 17.39

→ 51.87

Hence,

• Height of parallelogram = 17.29 cm
• Base of parallelogram = 51.87 cm