Question

8. Area of rectangle and area of square are equal. Perimeter of square is 64 cm. Breath of rectangle is 4 cm. What is the perimter of rectangle.​

Answer 1

Answer:

• Perimeter of rectangle is 136 cm.

Step-by-step explanation:

Given :-

• Area of rectangle and area of square are equal.
• Perimeter of square is 64 cm.
• Breadth of rectangle is 4 cm.

To find :-

• Perimeter of rectangle.

Solution :-

• First we will find side of square using perimeter.

• Area of square and area of rectangle are equal. So, then we will find length of rectangle using area of rectangle.

• Then, Finally we will find required perimeter.

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Perimeter of square = 4 × side

$\longrightarrow$ 64 = 4 × side

$\longrightarrow$ 64/4 = side

$\longrightarrow$ side = 16

Side of square is 16 cm

Area of square = Side × Side

$\longrightarrow$ Area = 16 × 16

$\longrightarrow$ Area = 256

Area of square is 256 cm².

It is given that,

Area of rectangle is equal to area of square.

So, Area of rectangle is 256 cm².

Area of rectangle = length × breadth

$\longrightarrow$ 256 = Length × 4

$\longrightarrow$ 256/4 = Length

$\longrightarrow$ Length = 64

Length of rectangle is 64 cm.

Now,

Perimeter of rectangle = 2(Length + Breadth)

$\longrightarrow$ Perimeter = 2 × (64 + 4)

$\longrightarrow$ Perimeter = 128 + 8

$\longrightarrow$ Perimeter = 136

Therefore,

Perimeter of rectangle is 136 cm.

Answer 2

Answer:

Given :-

• Area of rectangle and area of square are equal. Perimeter of square is 64 cm. Breadth of a rectangle is 4 cm.

To Find :-

• What is the perimeter of rectangle.

Solution :-

Given :

• Perimeter of a square = 64 cm
• Breadth of a rectangle = 4 cm

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

We know that,

★ Perimeter = 4 × side ★

According to the question by using the formula we get,

⇒ 4 × side = 64

⇒ side = 64/4

➠ side = 16 cm

Hence, the side of a square is 16 cm .

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

✪ Area of Square = (side)² ✪

Given :

• Side = 16 cm

According to the question by using the formula we get,

↦ Area = (16 cm)²

↦ Area = 16 cm × 16 cm

➦ Area = 256 cm²

Hence, the area of square is 256 cm² .

Again, we know that,

✫ Area of rectangle = L × B ✫

where,

• L = Length
• B = Breadth

Given :

• Area of rectangle = 256 cm²
• Breadth = 4 cm

According to the question by using the formula we get,

⇨ Area = L × B

⇨ 256 = L × 4

⇨ 256/4 = L

⇨ 64 = L

➡ L = 64 cm

Hence, the length of a rectangle is 64 cm

Last, we have to find the perimeter,

We know that,

❖ Perimeter of rectangle = 2(L + B) ❖

where,

• L = Length
• B = Breadth

Given :

• Length = 64 cm
• Breadth = 4 cm

According to the question by using the formula we get,

↪ Perimeter = 2(64 + 4)

↪ Perimeter = 2(68)

➲ Perimeter = 136 cm

∴ The perimeter of a rectangle is 136 cm .