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

$\red{\bigstar}$ 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.

Answer 2

Answer:

69Q:

The length of a rectangular hall is 5m more than its breadth. The area of the hall is 750 sq.m. The length of the hall is

A) 20

B) 25

C) 30

D) 35

Answer: C) 30

Explanation:

Let breadth = x m

Then, length = (x+5)m

Area of a rectangle = Length x Breadth

x(x+5) = 750

x² + 5x - 750= 0

(x+30)(x-25)= 0

x = 25 or x = -30

Hence, breadth x = 25m

=> Length = x + 5 = 25 + 5 = 30m.