Question

The Perimeter Of A Square Is Equal To The Perimeter Of A Rectangle If Side Of A Square Is 30cm.And Length Of A rectangle Is 40cm. Then Find The Breadth Of The Rectangle.​

Answer 1

ANSWER :

• ❖ If the perimeter of a square is equal to the perimeter of a rectangle and the side of square is 30 cm and length of the rectangle is 40 cm; then the breadth of the rectangle will be 20 cm.

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SOLUTION :

❒ Given :-

• Perimeter of the Square = Perimeter of the Rectangle

• Side of the Square = 30 cm

• Length of the Rectangle = 40 cm

❒ To Calculate :-

• Breadth of the Rectangle = ?

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❒ Required Formulas :-

• $\dag \: \: \underline{ \boxed{ \sf{ \: Perimeter \: \: of \: \: a \: \: Square = 4 \times Side \: }}}$

• $\dag \: \: \underline{ \boxed{ \sf{ \: Perimeter \: \: of \: \: a \: \: Rectangle = 2 (Length + Breadth) \: }}}$

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❒ Calculation :-

We have,

• Side of the Square = 30 cm

Using the formula of the Perimeter of a Square, we get,

• ★ Perimeter of the Square = 4 × Side

➨ Perimeter of the Square = 4 × 30 cm

➨ Perimeter of the Square = 120 cm

• So, the Perimeter of the Square = 120 cm

Again,

• Perimeter of the Square = Perimeter of the Rectangle

Hence,

• Perimeter of the Rectangle = 120 cm

We have,

• Length of the Rectangle = 40 cm

Using the formula of the Perimeter of a Rectangle, we get,

• ★ Perimeter of a Rectangle = 2 (Length + Breadth)

➜ 120 cm = 2 (40 cm + Breadth)

➜ 2 (40 cm + Breadth) = 120 cm

➜ 40 cm + Breadth = $\rm{\dfrac{120 \: cm}{2}}$

➜ 40 cm + Breadth = 60 cm

➜ Breadth = 60 cm - 40 cm

∴ Breadth = 20 cm

• Hence, the Breadth of the Rectangle is 20 cm.

Answer 2

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Answer = 20 cm

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Given

Perimeter of Rectangle = Perimeter of square

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Required Formula

Perimeter of square = 4× Side

Perimeter of Rectangle = 2 (length + breadth)

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Using formula of perimeter of square we get

4×Side

4×30

120 cm

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Again

perimeter of square = perimeter of Rectangle

Hence , perimeter of Rectangle = 120 cm

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Now we have length of Rectangle = 40 cm

Perimeter of Rectangle = 2 (l+b)

2(40+breadth) = 120

40 + Breadth = 120/2

40 + Breadth = 60

Breadth = 60-40

Breath = 20

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