Question

the lenth of a rectangular filed is 8m less than twice breadth . if the perimeter of rectangular filed is 56 meters, find is length and breadth?​

Answer 1

Correct Question:-

✯ The length of a rectangular field is 8 meter less than twice breadth . If the perimeter of rectangular field is 56 meters, find its length and breadth?

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Answer:-

$\pink{\bigstar}$ The parameters of the rectangular field are,

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

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

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• Given:-

• Length of rectangular field is 8 meter less than twice breadth.

• Perimeter of rectangular field is 56 metres.

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• To Find:-

• Length and breadth of the rectangular field.

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• Figure:-

$\setlength{\unitlength}{1cm}\begin{picture}(0,0)\thicklines\multiput(0,0)(5,0){2}{\line(0,1){3}}\multiput(0,0)(0,3){2}{\line(1,0){5}}\multiput(2.1,-0.7)(0,4.2){2}{\sf\large 2x-8 m}\multiput(-1.4,1.4)(6.8,0){2}{\sf\large x m}\put(-0.5,-0.4){\bf A}\put(-0.5,3.2){\bf D}\put(5.3,-0.4){\bf B}\put(5.3,3.2){\bf C}\end{picture}$

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• Solution:-

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

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• According to the question:-

✯ The length of the rectangular field is 8 meter less than twice the breadth.

Hence,

✯ $\large{\bf\pink{2x - 8}}$

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Now, we know

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

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• Substituting in the Formula:-

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➪ $\sf 56 = 2(2x - 8 + x)$

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➪ $\sf 56 = 2(3x - 8)$

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➪ $\sf 56 = 6x - 16$

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➪ $\sf 6x = 56 + 16$

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➪ $\sf 6x = 72$

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➪ $\sf x = \dfrac{72}{6}$

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★ $\large{\underline{\underline{\bf\red{ x = 12 \: m}}}}\dashrightarrow\bf\blue{[Breadth]}$

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• Now, length of the rectangular field:-

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➪ $\sf 2x - 8$

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➪ $\sf 2 \times 12 - 8$

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➪ $\sf 24 - 8$

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★ $\large{\underline{\underline{\bf\red{ 16 \: m}}}}\dashrightarrow\bf\blue{[Length]}$

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Therefore, the length and breadth of the rectangular field are 16 meter and 12 meter respectively.

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✯ Note:- Kindly, view the Answer from the website.

Answer 2

Given :-

• The length of a rectangular field is 8 m less than twice breadth. The perimeter of a rectangular field is 56 m.

To Find :-

• What is the length and breadth of a rectangular field.

Formula Used :-

$\sf\boxed{\bold{\pink{Perimeter\: of\: Rectangle =\: 2(Length + Breadth)}}}$

Solution :-

Let, the breadth be x m

And, the length will be 2x - 8 m

According to the question by using the formula we get,

↦ $\sf 2(2x - 8 + x) =\: 56$

↦ $\sf 2x - 8 + x =\: \dfrac{\cancel{56}}{\cancel{2}}$

↦ $\sf 2x + x - 8 =\: 28$

↦ $\sf 3x =\: 28 + 8$

↦ $\sf 3x =\: 36$

↦ $\sf x =\: \dfrac{\cancel{36}}{\cancel{3}}$

➠ $\sf\bold{\green{x =\: 12\: m}}$

Hence, the required length and breadth are :

➲ Breadth of a rectangular field :

↦ $\sf x\: m$

➦ $\sf\bold{\red{12\: m}}$

And,

➲ Length of a rectangular field :

↦ $\sf 2x - 8\: m$

↦ $\sf 2(12) - 8\: m$

↦ $\sf 2 \times 12 - 8\: m$

↦ $\sf 24 - 8\: m$

➦ $\sf\bold{\red{16\: m}}$

$\therefore$ The length and breadth of a rectangular field is 16 m and 12 m respectively.