Question

the area of a rectangular field is 1680 metre square. if length is 40 metre find the cost of fencing the boundary of the field at rupees15.25 per metre.
with step explanation plz​

Answer 1

Given :

The area of a rectangular field is 1680 metre square. The length is 40 metre. Cost of fencing the boundary of the field at rupees15.25 per metre.

To Find :

The cost of fencing.

Solution :

Analysis :

Here we first have to find the breadth of the rectangle from the area and length. Then we have to find the perimeter of the rectangle and then by multiplying the perimeter with the cost er can find the total cost.

Required Formula :

• Area of rectangle = Length × Breadth

• Perimeter of rectangle = 2(Length + Breadth)

Explanation :

Let us assume that the breadth is "b" m.

We know that if we are given the area and length of the rectangle and is asked to find the breadth then our required formula is,

Area of rectangle = Length × Breadth

where,

• Area = 1680 m²
• Length = 40 m
• Breadth = b m

Using the required formula and substituting the required values,

⇒ Area of rectangle = Length × Breadth

⇒ 1680 = 40 × b

⇒ 1680/40 = b

⇒ 168/4 = b

⇒ 42 = b

∴ b = 42 m.

The breadth of the field is 42 m.

Now the perimeter :

We know that if we are given the breadth and length of the rectangle and is asked to find the perimeter then our required formula is,

Perimeter of rectangle = 2(Length + Breadth)

where,

• Length = 40 m
• Breadth = 42 m

Using the required formula and substituting the required values,

⇒ Perimeter of rectangle = 2(Length + Breadth)

⇒ Perimeter of rectangle = 2(40 + 42)

⇒ Perimeter of rectangle = 2(82)

⇒ Perimeter of rectangle = 2 × 82

⇒ Perimeter of rectangle = 164

∴ Perimeter of rectangle = 164 m.

The cost :

We know that if we are given the perimeter of the rectangle and is asked to find the cost of fencing then our required formula is,

Cost = Cost per m × perimeter

where,

• Cost per m = ₹15.25
• Perimeter = 164 m

Using the required formula and substituting the required values,

⇒ Cost = Cost per m × perimeter

⇒ Cost = ₹15.25 × 164

⇒ Cost = ₹2501

∴ Cost = ₹2,501.

The cost of fencing the boundary of the rectangular field is ₹2,501.

Answer 2

Step-by-step explanation:

Given: The area of a rectangular field is 1680m². The length is 40m. Cost of fencing the boundary of the field at rupees 15.25 per metre.

Need to find: Cost of fencing ?

❏ In this question we have to find the cost of fencing. So first, we have to find the breadth then we have to find the perimeter and after that we easily find the cost of fencing by multiplying the perimeter with the given cost.

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__________________

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$\frak{\underline{\underline{\dag As\ we\ know\ that\ :-}}}$

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$\star\;\boxed{\sf{\pink{Area_{(rectangle)}\ =\ Length\ \times\ Breadth.}}}$

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$\bf {Here} \begin{cases} &\sf{Area\ =\ 1680m^2.} \\ &\sf{Length\ =\ 40m.} \\ &\sf{Breadth\ =\ b.} \end{cases}$

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Therefore,

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$\sf : \implies {\bigg [Area\ =\ Length\ \times\ Breadth \bigg]} \\ \\ \\ \sf : \implies {1680\ =\ 40\ \times\ b} \\ \\ \\ \sf : \implies {\dfrac{168 \cancel 0}{4 \cancel 0}\ =\ b} \\ \\ \\ \sf : \implies {\cancel \dfrac{168}{4}\ =\ b} \\ \\ \\ \sf : \implies {42\ =\ b} \\ \\ \\ \sf : \implies {\underline{\boxed{\purple{\bf b\ =\ 42m.}}}}\bigstar$

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$\sf \therefore {\underline{Hence,\ the\ breadth\ of\ the\ field\ is\ \bf 42m.}}$

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$\frak{\underline{\underline{\dag Now,\ finding\ the\ perimeter\ :-}}}$

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$\star\;\boxed{\sf{\pink{Perimeter_{(rectangle)}\ =\ 2(Length\ +\ Breadth).}}}$

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$\bf {Here} \begin{cases} &\sf{Length\ =\ 40m.} \\ &\sf{Breadth\ =\ 42m.} \end{cases}$

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Therefore,

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$\sf : \implies {\bigg [Perimeter\ =\ 2(Length\ +\ Breadth) \bigg]} \\ \\ \\ \sf : \implies {Perimeter\ =\ 2(40\ +\ 42)} \\ \\ \\ \sf : \implies {Perimeter\ =\ 2(82)} \\ \\ \\ \sf : \implies {Perimeter\ =\ 2\ \times\ 82} \\ \\ \\ \sf : \implies {\underline{\boxed{\purple{\bf Perimeter\ =\ 164m.}}}}\bigstar$

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$\sf \therefore {\underline{Hence,\ the\ perimeter\ of\ the\ field\ is\ \bf 164m.}}$

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$\frak{\underline{\underline{\dag Now,\ finding\ the\ cost\ of\ fencing\ :-}}}$

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$\star\;\boxed{\sf{\pink{Cost_{(fencing)}\ =\ Cost\ per\ m\ \times\ Perimeter.}}}$

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$\bf {Here} \begin{cases} &\sf{Cost\ per\ m\ =\ Rs.\ 15.25.} \\ &\sf{Perimeter\ =\ 164m.} \end{cases}$

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$\boldsymbol{\underline{\bigstar According\ to\ the\ question\ :-}}$

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$\sf : \implies {\bigg [Cost\ =\ Cost\ per\ m\ \times\ Perimeter \bigg]} \\ \\ \\ \sf : \implies {Cost\ =\ Rs.\ 15.25\ \times\ 164} \\ \\ \\ \sf : \implies {Cost\ =\ Rs.\ 2501.} \\ \\ \\ \sf : \implies {\underline{\boxed{\purple{\bf Cost\ =\ Rs.\ 2501.}}}}\bigstar$

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$\sf \therefore {\underline{Hence,\ the\ cost\ of\ fencing\ the\ rectangular\ field\ is\ \bf Rs.\ 2501.}}$