Question

The length of a rectangular hall is 4 metres more than its breadth. If the perimeter of the hall is 56 metres, find its length and breadth.​

Answer 1

☆GIVEN☆

• The length of a rectangular hall is 4 metres more than its breadth.
• The perimeter of the hall is 56 metres.

☆TO FIND☆

Length and breadth.

☆SOLUTION☆

Let the breadth be (x) m.

Length = (x + 4) m.

We know that,

$\large{\red{\underline{\boxed{\bf{Perimeter=2(length+breadth)}}}}}$

According to the question,

$\large\implies{\sf{Perimeter=2(length+breadth)}}$

$\large\implies{\sf{56=2(x+4+x)}}$

$\large\implies{\sf{56=2(2x+4)}}$

$\large\implies{\sf{56=4x+8}}$

$\large\implies{\sf{56-8=4x}}$

$\large\implies{\sf{48=4x}}$

$\large\implies{\sf{\dfrac{48}{4}=x}}$

$\large\implies{\sf{\dfrac{\cancel{48}}{\cancel{4}}=x}}$

$\large\implies{\sf{12=x}}$

$\large\therefore\boxed{\bf{x=12}}$

Therefore,

1. Breadth = x = 12 m.
2. Length = x + 4 = 12 + 4 = 16 m.

☆VERIFICATION☆

$\large\implies{\sf{Perimeter=2(length+breadth)}}$

$\large\implies{\sf{56=2(16+12)}}$

$\large\implies{\sf{56=2\times28}}$

$\large\implies{\sf{56=56}}$

$\large\therefore\boxed{\bf{LHS=RHS}}$

Hence verified.

$\large{\red{\underline{\boxed{\bf{Length\:of\:the\:rectangular\:hall\:is\:16\:m.}}}}}$

$\large{\red{\underline{\boxed{\bf{Breadth\:of\:the\:rectangular\:hall\:is\:12\:m.}}}}}$

Answer 2

Answer:-

$\red{\bigstar}$ Length $\large\leadsto\boxed{\tt\purple{16 \: m}}$

$\red{\bigstar}$ Breadth $\large\leadsto\boxed{\tt\purple{12 \: m}}$

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• Given:-

• Length of rectangular hall is 4m more than its breadth.

• Perimeter of the hall is 56m.

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• To Find:-

• Length and breadth of the rectangular hall.

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• Solution:-

Let the breadth of the rectangular hall be 'x'.

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Given that,

Length of the rectangular hall is 4 metres more than its breadth.

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Therefore,

Length of the rectangular hall is 'x+4'.

★ Figure:-

$\setlength{\unitlength}{1cm}\begin{picture}(0,0)\thicklines\multiput(0,0)(5,0){2}{\line(0,1){3}}\multiput(0,0)(0,3){2}{\line(1,0){5}}\put(2,3.5){\sf\large x+4 m}\put(-1.4,1.4){\sf\large x m}\put(2,1.4){\large\bf 56 m}\put(-0.5,-0.4){\bf A}\put(-0.5,3.2){\bf D}\put(5.3,-0.4){\bf B}\put(5.3,3.2){\bf C}\end{picture}$

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We know,

$\pink{\bigstar}$ $\large\underline{\boxed{\bf\green{Perimeter = 2(l+b)}}}$

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➪ $\sf 56 = 2((x+4) + x)$

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➪ $\sf 56 = 2(x + 4 + x)$

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➪ $\sf 56 = 2(2x+4)$

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➪ $\sf 56 = 4x + 8$

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➪ $\sf 4x = 56 - 8$

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➪ $\sf 4x = 48$

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➪ $\sf x = \dfrac{48}{4}$

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★ $\large{\bf\pink{12}}$

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Hence,

• Length = x + 4 → 12 + 4 → 16 m

• Breadth = 12 m

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Therefore, the length and breadth of the rectangular hall is 16m and 12m respectively.