Question

20 cm. 8. A rectangular piece of plot measures 0.6 km by 0.5 km. Each side is to be fenced with 5 rows of wires. What is the length of the wire needed? If the wire costs 7 9 per metre, what will be the cost of the wire required for fencing?
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Answer 1

Given :

• Length of plot = 0.6 km
• Breadth of plot = 0.5 km
• Each side is to be fenced with 5 rows of wires .
• Cost of wire = 79 per m²

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To Find :

• Measure of wire required = ?
• Cost of wire = ?

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Solution :

~ Formula Used :

${\red{\dashrightarrow}} \: \: {\underline{\boxed{\purple{\sf{ Perimeter{\small_{(Rectangle)}} = 2(Length + Breadth) }}}}}$

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~ Concept Used + How to Solve :

We will apply the concept of Perimeter here as the plot has to be fenced .After that ,We will Multiply the Perimeter with No. of times the plot has to be fenced (5) .We will get the total wire required and by multiplying this wire with cost of wire we will the Total cost of wire required . Let's Solve :

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~ Converting the Values :

1000 m = 1 km .So,

• 0.6 km = 600 m
• 0.5 km = 500 m

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~ Calculating the Perimeter of Plot :

${\longmapsto{\qquad{\sf{ Perimeter{\small_{(Plot)}} = 2(Length + Breadth) }}}} \\ \\ \ {\longmapsto{\qquad{\sf{ Perimeter {\small_{(Plot)}} = 2(600 + 500)}}}} \\ \\ \ {\longmapsto{\qquad{\sf{ Perimeter {\small_{(Plot)}} = 2 \times 1100 }}}} \\ \\ \ {\qquad{\textsf{ Perimeter of the Plot = {\color{maroon}{\sf{ 2200 \: m }}}}}}$

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~ Calculating the Wire Required :

${:\implies{\qquad{\sf{ Wire \: Required = Perimeter {\small_{(Plot)}} \times No. \: of \: Times }}}} \\ \\ \ {:\implies{\qquad{\sf{ Wire \: Required = 2200 \times 5 }}}} \\ \\ \ {\qquad{\textsf{ Wire Required to fence the Plot = {\orange{\sf{ 11000 \: m }}}}}}$

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~ Calculating the Cost of Wire :

${\longmapsto{\qquad{\sf{ Cost{\small_{(Wire)}} = Wire \: Required \times Rate \: of \: Wire }}}} \\ \\ \ {\longmapsto{\qquad{\sf{ Cost{\small_{(Wire)}} = 11000 \times 79 }}}} \\ \\ \ {\qquad{\textsf{ Cost of the wire Required = {\green{\sf{ ₹ 869000 }}}}}}$

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Therefore :

❝ Measure of wire required is 11000 m and its cost is ₹ 869000 . ❞

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${\pmb{\frak{ Note \: :- }}}$ Refer to Attachment for the figure .