Question

2. 44. A square and a rectangle have the same perimeter. If the side of the square is 16 m and the length of the rectangle is 18 m, the breadth of the rectangle is (A) 14 m (B) 15 m (C) 16 m (D) 17 m
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Answer 1

$\large \clubs \:  \bf Given :  -$

• A square and a rectangle have the same perimeter.

• The side of the square is 16 m

• The length of the rectangle is 18 m.

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$\large \clubs \:  \bf To \: Find :  -$

• The Breadth of the Rectangle

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$\large \clubs \:  \bf Formulae \:   Used:  -$

✏ Perimeter of Square :

$\large \text{P}_{ \text{(Square)}} = \text{4a }$

Where

• a = Side Length of the Square

✏ Perimeter of Rectangle :

$\large\text P_{\text{(Rectangle)}}\text{ = 2(l + b)}$

Where ,

• l = Length of Rectangle

• b = Breadth of Rectangle

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$\large \clubs \:  \bf Solution :  -$

We Have,

• Side of Square = a = 16 m

Hence,

$\large\text{P}_{ \text{(Square)}} = \text{4a } \\ \\ \large = 4 \times 16$

$\purple{ \Large :\longmapsto  \underline {\boxed{{\bf {P}_{{(Square)}} = {64 \: {m} }} }}}$

Also,

Length of Rectangle = l = 18m

Let Breadth of Rectangle = b

Hence,

$\large\text P_{\text{(Rectangle})}\text{ = 2(18 + b)}$

$\purple{ \large:\longmapsto \underline {\boxed{{\bf P_{{Rectangle}}{ = 36 + 2b}} }}}$

✏ According To Question :

$\large\red{\text{P}_{ \text{(Square)}} = \text P_{\text{(Rectangle)}}}$

$:\longmapsto64 = 36 + 2 \text b$

$:\longmapsto2 \text b = 28$

$:\longmapsto \text b = \cancel \dfrac{28}{2}$

$\purple{ \Large :\longmapsto  \underline {\boxed{{\bf b = 14} }}}$

Hence,

$\large\underline{\pink{ \underline{ \pmb{\frak{Breadth \: of \: Rectangle = 14 \: m }}}}}$

$\large\underline{\pmb{ \green{ \underline{\mathfrak { \text So \: Option \: \text A \: is \: Correct }}}}}$

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Answer 2

Question

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A square and a rectangle have the same perimeter. If the side of the square is 16 m and the length of the rectangle is 18 m, then breadth of the rectangle is :

• (A) 14 m

• (B) 15 m

• (C) 16 m

• (D) 17 m

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Answer

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• Option (A) 14 m is correct.

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Step - By - Step Explanation

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Given that

$\:$

• Perimeter of square = Perimeter of rectangle.

• Side of square = 16 m.

• Length of rectangle (ℓ) = 18 m.

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To Find

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• Breadth of rectangle (b)?

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Solution

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$\clubsuit$ Formulae Used

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• Perimeter (square) = 4 × side

• Perimeter (rectangle) = 2(ℓ + b)

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★ Finding perimeter of square :

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➦ ㅤPerimeter (square) = 4 × side

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➦ ㅤPerimeter (square) = 4 × 16

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➦ㅤ Perimeter (square) = 64

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• Therefore, perimeter of square is 64 m².

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★ According to the Question :

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➥ Perimeter of rectangle = Perimeter of square

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➥ㅤ 2(ℓ + b) = 64

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➥ㅤ 2(18 + b) = 64

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➥ㅤ (2 × 18) + (2 × b) = 64

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➥ㅤ 36 + 2b = 64

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➥ㅤ 2b = 64 - 36

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➥ㅤ 2b = 28

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➥ㅤ b = $\sf {\cancel{\dfrac{28}{2}}}$

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➥ㅤ b = 14

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• Therefore, breadth of rectangle is 14 m. So, Option (A) 14 m is correct.

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Know More

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• Perimeter of rectangle = 2(ℓ + b)

• Perimeter of square = 4 × side

• Perimeter of circle = 2πr

• Perimeter of equilateral ∆ = 3 × side

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