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

Step-by-step explanation:

Answer:-

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

16m

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

12m

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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)}}}

Perimeter=2(l+b)

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➪ \sf 56 = 2((x+4) + x)56=2((x+4)+x)

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➪ \sf 56 = 2(x + 4 + x)56=2(x+4+x)

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➪ \sf 56 = 2(2x+4)56=2(2x+4)

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➪ \sf 56 = 4x + 856=4x+8

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➪ \sf 4x = 56 - 84x=56−8

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➪ \sf 4x = 484x=48

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➪ \sf x = \dfrac{48}{4}x=

4

48

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★ \large{\bf\pink{12}}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.

Answer 2

$\huge{ \underline{ \bf{Given \: : }}}$

• Length of the rectangle hall is 4 metres more than its breadth

• perimeter of the hall is 56 meters

$\huge{ \underline{ \bf{To \: Find \: : }}}$

• Length and breadth

$\huge{ \underline{ \bf{Solution \: : - }}}$

Let the breadth of the hall be X

And let the length of the hall be

x + 4

As we know,

Perimeter of a rectangle

$\red{ \underline{ \underline{ \boxed{ \tt{ \green{Perimeter = 2(length + breadth)}}}}}}$

$\tt \to56 =2(x + (x + 4))$

$\tt \to \cancel \frac{56}{2} = x + x + 4$

$\tt \to28 = 2x + 4$

$\tt \to2x = 28 - 4$

$\tt \to2x = 24$

$\tt \to \: x = \cancel \frac{24}{2}$

$\tt \to \: x = 12$

Therefore,

• Breadth = 12m
• Length = (x + 4) = 12 + 4 = 16m