Question

The area of a parallelogram is equal to the area of a square whose perimeter is 140 cm. If the height of

the parallelogram is 25 cm, then find its corresponding base.​

Answer 1

Answer:

• Corresponding base is 49 cm.

Step-by-step explanation:

Given :-

• Area of parallelogram and area of square are equal.
• Perimeter of square is 140 cm.
• Height of parallelogram is 25 cm.

To find :-

• Corresponding base of parallelogram.

Solution :-

Perimeter of square = 4 × side

⇒140 = 4 × side

⇒140/4 = side

⇒ side = 35

Side of square is 35 cm.

Area of square = Side × Side

⇒35 × 35

⇒1225

Area of square is 1225 cm².

Area of parallelogram is equal to area of square.

Thus,

Area of parallelogram is 1225 cm².

Area of parallelogram = Base × height

So,

⇒1225 = base × 25

⇒1225/25 = base

⇒h = 49

Therefore,

Length of corresponding base is 49 cm.

Answer 2

Answer:

Given :-

• The area of a parallelogram is equal to the area of a square whose perimeter is 140 cm.
• The height of the parallelogram is 25 cm.

To Find :-

• What is the corresponding base.

Solution :-

First, we have to find the side of a square,

Given :

• Perimeter of a square = 140 cm

We know that,

★ Perimeter = 4 × side ★

According to the question by using the formula we get,

↦ 4 × side = 140

↦ side = 140 ÷ 4

➠ side = 35 cm

Hence, the side of a square is 35 cm .

Now, we have to find the area of a square,

We know that,

✰ Area = side × side ✰

We get,

• Side = 35 cm

According to the question by using the formula we get,

⇒ Area = 35 cm × 35 cm

➦ Area = 1225 cm²

Hence, the area of a square or area of a parallelogram is 1225 cm²

Again,

We know that,

✪ Area of parallelogram = B × H ✪

where,

• B = Breadth
• H = Height

Given :

• Height = 25 cm
• Area of parallelogram = 1225 cm²

According to the question by using the formula we get,

↣ A = B × H

↣ 1225 = B × 25

↣ 1225 ÷ 25 = B

↣ 49 = B

➲ B = 49 cm

∴ The corresponding base of a parallelogram is 49 cm.