Question

The perimeter of a parallelogram is 35 cm. If the ratio of two side of the parallelogram is 2 : 3 .find the length of the side of the parallelogram.​

Answer 1

Given:

A parallelogram with

• Perimeter = 35 cm
• Ratio of two side = 2 : 3

What To Find:

We have to find the length.

How To Find:

To find the length of the parallelogram. We wil

• Take x as the common multiple of the ratio 2 : 3 = 2x : 3x.
• Next the perimeter of parallelogram is sum of all four sides.
• Then the equation will be 2x + 3x + 2x + 3x = 35 cm.
• Finally, substitute the values.

Solution:

2x + 3x + 2x + 3x = 35 cm

Add the terms in LHS,

⇒ 10x = 35 cm

Take 10 to RHS,

⇒ x = $\dfrac{35}{10}$

Divide 35 by 10,

⇒ x = 3.5 cm

Now, substitute the values,

• 2x = 2 × 3.5 = 7 cm
• 3x = 3 × 3.5 = 10.5 cm

∴ Hence, the length of the side of the parallelogram are 7 cm and 10.5 cm.

Verification:

2x + 3x + 2x + 3x = 35 cm

Substitute the values,

⇒ 2(3.5) + 3(3.5) + 2(3.5) + 3(3.5) = 35

Solve the brackets,

⇒ 7 + 10.5 + 7 + 10.5 = 35

Add the numbers,

⇒ 35 = 35

∴ LHS = RHS

∴ Hence, verified.

Answer 2

Answer:

The length of the parallelogram is 7cm

Step-by-step explanation:

Question says that,

Dimensions of the parallelogram is in ratio :

→ Length : Breadth

→ 2 : 3

• Perimeter is 35cm.

Find the length of the parallelogram.

Step 1 : Let's assume the dimensions of the parallelogram :

➪ Length = $2x$cm.

➪ Breadth = $3x$cm.

Step 2 : Calculate the perimeter :

Perimeter of a parallelogram is given by :

$\mathcal P = 2(l + b)$

Where,

• $\mathcal P = \sf perimeter$
• $l {\sf{ (length)}} = 3x$
• $b {\sf{ (breadth)}} = 2x$

$\mathcal P = 2(3x + 2x)$

$\mathcal P = 2(5x)$

$\mathcal P = 10x$

Step 3 : Calculate the dimensions of the parallelogram :

The perimeter of the parallelogram is $10x$ cm.

But, the perimeter is 35cm. (given)

So, we can say that,

$\implies 10x = 35$

Solving for $x$ :

$\implies 10x = 35$

$\implies x = \dfrac{35}{10}$

$\implies x = 3.5$

$\therefore x = \bf 3.5 cm$

Therefore the dimensions of parallelogram will be :

➪ length = $2x = \bf 2(3.5) = 7cm$

➪ breadth = $3x = \bf 3(3.5) = 10.5cm$