Question

PQRS is a parallelogram, in which PQ = 12 cm and its perimeter is 40 cm. Find the length of each side of the parallelogram.​

Answer 1

Question:-

PQRS is a parallelogram, in which PQ = 12 cm and its perimeter is 40 cm. Find the length of each side of the parallelogram.

Answer:-

• PS = QR = 8 cm
• PQ = SR = 12 cm

To find :-

• All sides of parallelogram

Solution:-

• PQ = SR = 12 cm ( Opposite sides of parallelogram are equal)
• PS = QR = x
• Perimeter = 40 cm

$\blue{ \underline{ \underline { \green{ \large{ \mathfrak{ perimeter = 2(l + b)}}}}}}$

Here,

• l = PQ = SR = 12 cm
• b = PS = QR = x

According to question,

$\large{ \tt : \implies \: \: \: \: \: 2(12 + x) = 40}$

$\large{ \tt : \implies \: \: \: \: \: 12 + x = \frac{40}{2} }$

$\large{ \tt : \implies \: \: \: \: \: 12 + x = 20}$

$\large{ \tt : \implies \: \: \: \: \: x = 20 - 12}$

$\large{ \tt : \implies \: \: \: \: \: x = 8 \: cm}$

• The value of x is 8 cm
• PS = QR = x = 8 cm
• PQ = SR = 12 cm

Answer 2

Answer :

• All sides of the parallelogram are 12cm, 8cm, 12cm and 8cm respectively.

Given :

• PQRS is a parallelogram, in which PQ = 12 cm and its perimeter is 40 cm.

To Find :

• Length of each side of the parallelogram.

Solution :

Suppose PQRS is a parallelogram in which

• PQ = RS = 12cm

Here

• Perimeter of the parallelogram is 40cm

Let

• PQ = RS = a
• QR = RP = b

We've to find QR and RP.

As we know that

Perimeter of a parallelogram is

• 2 (a + b)

According to question :

→Perimeter of the parallelogram = 40

→ 2 (12 + b) = 40

→ 12 + b = 40/2

→ 12 + b = 20

→ b = 20 - 12

→ b = 8

Now

• QR = RP = b = 8cm

Hence, all sides of the parallelogram are 12cm, 8cm, 12cm and 8cm respectively.