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.

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Answer 1

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.