Question

The length and breadth of a rectangular field are in the ratio of 7.5 if its perimeter is 480m,finds its dimensions.

Answer 1

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Answer 2

Answer:-

$\red{\bigstar}$ Dimensions of rectangular field are $\large\leadsto\boxed{\tt\purple{140 \times 100 \: m^2}}$

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• Given:-

• Ratio of length and breadth of a rectangular field = 7:5

• Perimeter of rectangular field = 480 m

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• To Find:-

• Dimensions of the rectangular field.

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• Solution:-

Let the length and breadth in the ratio be '7x' and '5x' respectively.

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★ Figure:-

$\setlength{\unitlength}{1cm}\begin{picture}(0,0)\thicklines\multiput(0,0)(5,0){2}{\line(0,1){3}}\multiput(0,0)(0,3){2}{\line(1,0){5}}\multiput(2.1,-0.7)(0,4.2){2}{\sf\large 7x m}\multiput(-1.4,1.4)(6.8,0){2}{\sf\large 5x m}\put(-0.5,-0.4){\bf A}\put(-0.5,3.2){\bf D}\put(5.3,-0.4){\bf B}\put(5.3,3.2){\bf C}\end{picture}$

• According to the question:-

Perimeter of the rectangular field is 480 m.

We know,

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

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• Substituting in the values:-

➪ $\sf 480 = 2(7x + 5x)$

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➪ $\sf 480 = 2(12x)$

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➪ $\sf 480 = 24x$

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➪ $\sf x = \dfrac{480}{24}$

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★ $\large{\bf\pink{x = 20}}$

Hence,

• Length = 7x = 7 × 20 = 140 m

• Breadth = 5x = 5 × 20 = 100 m

Therefore, the dimensions of the rectangular field are 140 × 100 m².