Question

7. The perimeter of a rectangle of sides 24 cm
and 16 cm is equal to the perimeter of a
square. Find the side and area of the square.​

Answer 1

Given

• Length of rectangle = 24 cm
• Breadth of rectangle = 16 cm
• Perimeter of rectangle is equal to the perimeter of square.

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To find

• Side of the square.
• Area of the square.

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Explanation

• In this question, we will solve the question in three parts.

⠀⠀⠀❍ Part 1

→ We will find the perimeter of rectangle by using the given values of length and breadth.

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⠀⠀⠀❍ Part 2

→ Since, the perimeter of rectangle and square is same. Hence, we can easily find the measure of each side of the square.

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⠀⠀⠀❍ Part 3

→ After finding the side, we can calculate the area of the square.

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Solution

• It is given in the question that length and breadth of the rectangle is 24cm and 16cm respectively.

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$\: \: \boxed{\tt{\bigstar{Perimeter_{(Rectangle)} = 2(l + b){\bigstar}}}}$

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$\tt\longrightarrow{Perimeter = 2(24 + 16)}$

$\tt\longrightarrow{Perimeter = 2 \times 40}$

$\bf\longrightarrow{Perimeter = 80 cm}$

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• Since, the perimeter of rectangle and square is equal.

$\boxed{\sf{\orange{Perimeter_{(Rectangle)} = Perimeter_{(Square)}}}}$

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• We have, perimeter of square is 80cm.

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$\: \: \: \: \: \: \boxed{\tt{\bigstar{Perimeter_{(Square)} = 4 \times side{\bigstar}}}}$

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$\tt\longrightarrow{Perimeter = 80}$

$\tt\longrightarrow{4(side) = 80}$

$\bf\longrightarrow{side = 20}$

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★ Hence,

• Each side of square is 20 cm.

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• Now, we will find area of the square.

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$\: \: \: \: \: \: \: \: \: \: \: \: \boxed{\tt{\bigstar{Area_{(Square)} = (Side)^2{\bigstar}}}}$

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$\tt\longmapsto{Area = (20)^2}$

$\bf\longmapsto{Area = 400}$

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★ Hence,

• Area of the square is 400 cm².

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Answer 2

AnswEr :

• Side of the square = 20cm
• Area of the square = 400cm

Given :

• The perimeter of a rectangle of sides 24cm and 16cm is equal to the perimeter of a square.

To Find :

• Side and area of the square.

Solution :

Here

• Length = 24cm ; Breadth = 16cm
• Perimeter of the rectangle = Perimeter of the square.

As we know that

• Perimeter of a rectangle = 2 (l + b)

Where

• l = length
• b = breadth

Now

→ Perimeter of the rectangle = 2 (l + b)

→ Perimeter of the rectangle = 2 (24 + 16)

→ Perimeter of the rectangle = 2 × 40

→ Perimeter of the rectangle = 80cm

°.° Perimeter of the rectangle = Perimeter of the square = 80cm

As we know that

• Perimeter of the square = 4 × side

Now

→ Perimeter of the square = 4 × side

→ 80 = 4 × side

→ 80/4 = side

→ side = 20cm

As we know that

• Area of a square = side²

According to question :

→ Area of the square = side²

→ Area of the square = (20)²

→ Area of the square = 20 × 20

→ Area of the square = 400cm²

Hence, the side and area of the square are 20cm and 400cm² respectively.