Question

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the length and breadth of a rectangular field are the ratio 3:2 it is the area of the field is 3456 m find the cost of fencing the field 4.50 per metre

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Answer 1

QUESTION :

• ➫ The length and breadth of a rectangular field are the ratio 3:2. The area of the field is 3456 square metre. Find the cost of fencing the field at Rs. 4.50 per metre.

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SOLUTION :

❖ Given :-

• Ratio of length and breadth of the rectangular field = 3 : 2

• Area of the rectangular field = 3456 square metre

• Cost of fencing the field per metre = Rs. 4.50

❖ To Find :-

• Cost of fencing the whole rectangular field = ?

❖ Required formulas :-

$\bigstar \: \: \boxed{ \rm{ \: Area \: \: of \: \: rectangle = Length \times Breadth \: }} \: \: \: \: \: \: \: \: \\ \\ \: \: \: \: \: \: \bigstar \: \: \boxed{ \rm{ \: Perimeter \: \: of \: \: rectangle = 2 \: (Length + Breadth) \: }}$

❖ Calculation :-

Suppose,

• The length of the rectangular field, l = 3x

• The breadth of the rectangular field, b = 2x

According to question,

$\: \: \: \: \bigstar \: \: \sf{ \large{Length \times Breadth = Area }} \\ \\ \sf{ \large{ \implies \: 3x \times 2x = 3496}} \: \: \: \: \: \: \: \\ \\ \sf{ \large{ \implies \: 6x {}^{2} = 3456}} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \sf{ \large{ \implies \: x {}^{2} = \dfrac{3456}{6} }} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \sf{ \large{ \implies \: x {}^{2} = 576}} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \sf{ \large{ \implies \: x = \sqrt{576} }} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \sf{ \large{ \therefore \: x = 24}} \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

Hence,

$\: : \mapsto \: \bold{ Length,l =3x = 3 \times 24 = \underline{ \: 72 \: m \: }} \\ \\ \: : \mapsto \: \bold{ Breadth,b = 2x = 2 \times 24 = \underline{48 \: m \: }}$

Again,

$\bigstar \: \: \sf{Perimeter \: \: of \: \: the \: \: rectangular \: \: field = 2 \: (l + b) }\\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf{ = \{2 \: (72 + 48) \} \: \: m} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf{ = (2 \times 120) \: \: m} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf{ = 240 \: \: m}$

Now,

$\bigstar \: \: \sf{Cost \: \: of \: \: fencing \: the \: \: field \: \: per \: \: metre = Rs. \: 4.50} \: \: \: \: \: \: \: \: \: \: \: \\ \\ \: \: \: \sf{ \therefore \: Cost \: \: of \: \: fencing \: \: the \: \: field \: \: of \: \: 240 \: m = Rs. \: (240 \times 4.50)} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf{ = \underline{ \: Rs. \: 1080 \: }}$

• Hence, the cost of fencing the rectangular field at Rs. 4.50 per metre is Rs. 1080.

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ANSWER :

• ➬ If the length and breadth of a rectangular field are the ratio 3:2 and the area of the field is 3456 square metre, then the cost of fencing the field at Rs. 4.50 per metre is Rs. 1080.