Question

There is a narrow rectangular plot reserved for a school in mahuli village. The length and breadth of the plot are in the ratio 11:4. At the rate rupees 100 per metre it will cost the village Panchayat rupees 75000 to fence the plot. What are the dimensions of the plot ?

Answer 1

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${\large{\blue{\bold{\underline{Given:-}}}}}$

▪︎ Length and breadth are in ratio 11:4.

▪︎ Cost of fencing one meter = Rupees 100.

▪︎ Total cost of fencing = Rupees 75000.

${\large{\blue{\bold{\underline{Now,}}}}}$

▪︎ Let the length of school be 11x.

▪︎ Let the breadth of school be 4x.

${\large{\blue{\bold{\underline{So,}}}}}$

▪︎ From the question we get,

$\implies \: 100 \times( 2(l + b)) = 75000 \\ \\ \implies \: 100 \times (2(11x + 4x)) = 75000 \\ \\ \implies \: 100 \times (2(15x) = 75000 \\ \\ \implies100 \times 30x = 75000 \\ \\ \implies3000x = 75000 \\ \\ \implies \: x = 75000 \div 3000 \\ \\ \implies \: x = 75 \div 3 \\ \\ \implies \: x = 25.$

${\large{\blue{\bold{\underline{Therefore,}}}}}$

▪︎Length,

$= 11x \\ \\ = 11(25) \\ \\ = 275m.$

▪︎ Breadth,

$= 4x \\ \\ = 4(25) = 100m.$

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Answer 2

Answer:

Length=275 m

Breadth=100 m

Step-by-step explanation:

Given :-

1. Ratio of Length and Breadth = 11 : 4
2. Cost of fencing = 75000

To Find:-

Dimensions of the plot.

Solution :-

Length = 11x m.

Breadth = 4x m.

• Perimeter of rectangular plot  = 2 (Length + Breadth)

• Perimeter of rectangular plot  = 2 (11x + 4x)

• Perimeter of rectangular plot  = 30x m

• Cost of fencing = Perimeter × Rate per meter
• 75,000 = 30x × 1000
• 75,000 = 3000x
• 75000/3000 = x
• 75/3=x
• 25 = x
• Length = 11 × 25 = 275 m
• Breadth = 4 × 25 = 100 m