Question

Perimeter of a square room is 56 m. Another room has one side 2 m more than the first
but has the same perimeter. Find the length and breadth of the second room​

Answer 1

$\underline{\underline{\huge{\gray{\tt{\textbf Answer :-}}}}}$

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$\sf\large\bold{\orange{\underline{\blue{ Given :-}}}}$

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• Perimeter of a square room is 56 m

• Other room has one side 2 m more than the first

• The other room has the same perimeter as that of square room

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$\sf\large\bold{\orange{\underline{\blue{ To \: Find :-}}}}$

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• Length and breadth of the second room

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$\sf\large\bold{\orange{\underline{\blue{ Solution :-}}}}$

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• Let one side of second room be 'b'

• So , the other side will be 'b + 2'

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Clearly the second room is rectangular as the length and breadth differs

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$\underline{\bold{\texttt{Perimeter of rectangle :}}}$

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➠ P = 2(l + b) ⚊⚊⚊⚊ ⓵

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Where ,

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• P = Perimeter

• l = Length

• b = Breadth

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$\underline{\bold{\texttt{For second room :}}}$

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Given that the perimeter is same as that of square room i.e 56 m

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Let length be 'b + 2'

Let breadth be 'b'

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So,

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• P = 56 m

• l = b + 2

• b = b

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⟮ Putting the above values in ⓵ ⟯

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➜ P = 2(l + b)

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➜ 56 = 2(b + 2 + b)

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➜ 56 = 2(2b + 2)

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➜ 56 = 4b + 4

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➜ 4b = 56 - 4

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➜ 4b = 52

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➜ $\sf b = \dfrac { 52 } { 4 }$

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➨ b = 13 m

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• Hence the breadth of second room is 13 m

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Length of second room will be (13 + 2)m

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• Hence the length of second room is 15 m

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∴ The length and breadth of second room is 15 m & 13 m