Question

length and breadth of a rectangular field is in the ratio of4x and 3x and the area is 4800 find the cost of fencing it at 80 ruppes per metre​

Answer 1

Given:

• length and breadth of a rectangular field is in the ratio of 4x : 3x

• The area of the rectangular field is 4800m²

To Find:

• The cost of fencing the field at the rate rupees 80 per meter

Understanding the question

Now, here we have given the ratio of the dimensions and the area of the field and said to find the cost of fencing the field so, firstly let's find the dimensions of the field so, that we can the the perimeter of the field and than the cost to fence the field .

Solution:

${ \purple{ \underline{ \frak{As \: we \: know \: that : }}}}$

$\blue{ \underline{ \boxed{ \pink{ \mathfrak{ area \: of \: a \: rectangle = lenght \times breadth}}}}}$

Let's substitute the values now,

$\longrightarrow \tt area = l \times b \: \: \: \: \: \\ \\ \\ \longrightarrow \tt 4800 = 4x \times 3x \\ \\ \\\longrightarrow \tt 4800 = 12 {x}^{2} \: \: \: \: \: \\ \\ \\ \longrightarrow \tt {x}^{2} = \cancel\frac{4800}{12} \: \: \: \: \: \: \: \: \\ \\ \\ \longrightarrow \tt \: {x}^{2} = 400 \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\\longrightarrow \tt x = \sqrt{400} \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ \longrightarrow { \boxed{\tt {x = 20}}} \: \: \: \: \: \: \: \: \: \:$

Hence The dimensions are,

• ➪${ \bf{ \pink{lenght = 4x = 80m}}}$
• ➪${ \bf{ \pink{breadth = 3x = 60m}}}$

✪ Now, let's find Cost to fence the rectangle,

${\longrightarrow }\tt cost \: to \: fence = \bigg( 2(l + b) \bigg)\times 80 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ {\longrightarrow }\tt cost \: to \: fence = \bigg( 2(80+ 60) \bigg)\times 80 \\ \\ \\ {\longrightarrow }\tt cost \: to \: fence = \bigg( 2(140) \bigg)\times 80 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ \longrightarrow \tt cost \: to \: fence = 280 \times 80 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ \longrightarrow \tt cost \: to \: fence = 22,400 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

$\orange{\underline{\frak{Hence \: the\:cost\:to\:fence\: is\: rs.22400}}}$

Answer 2

A N A L Y S I S :-

‎ ‎ ‎ ‎ ‎ ‎ ‎The ratio of length and breadth of a rectangular field has been given along with the measure of its area. The field has to be fenced at the rate of 80 per metre. And we're asked to find the cost of fencing the field.

• Ratio of length to breadth of the field is 4x : 3x.
• Area of the field is 4800 m².

How can we find it? We know that fencing is done in the boundaries of the fields. So as per it we can uphold that the perimeter of the field should be known to find the cost of fencing. And in our question, we don't know the perimeter or the length and breadth to find the perimeter.

First we shall be finding the length and breadth of the field by using the given data and then we will be finding the perimeter. And finally, the cost of fencing will be determined by us. Let's start doing!

S O L U T I O N :-

➜ Finding the length and breadth of the field:

‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎This can be done by terming the values of length and breadth of the field as 4x and 3x, respectively and equating these measures in the formula of area of rectangle along with other known measures (area of the field).

$\longmapsto{ \sf{ \pmb{Area_{(rectangle)} = l \times b}}} \\ \\ \longmapsto{ \sf{4800 = (4x) \times (3x)}} \\ \\ \longmapsto{ \sf{4800 = 12 {x}^{2} }} \\ \\ \longmapsto{ \sf{ \dfrac{ \cancel{4800}}{ \cancel{12}} = {x}^{2} }} \\ \\ \longmapsto{ \sf{400 = {x}^{2} }} \\ \\ \longmapsto{ \sf{ \sqrt{400} = x }} \\ \\ \longmapsto \boxed{ \tt{ \purple{ \pmb{20 = \sf{x}}}}}$

As we know the value of x, we can find the measures of length and breadth by substituting the value of x in the expressions of length and breadth.

$\Rightarrow{ \sf{Length \: (4x) = 4 \times 20 = \underline{ \pmb{80 \: m}}}} \\ \Rightarrow{ \sf{Breadth \: (3x) = 3 \times 20 = \underline{ \pmb{60 \: m}}}}$

‎

➜ Finding the perimeter of the field:

On substituting the measures of length and breadth in the formula,

$\longmapsto{ \sf{Perimeter = 2(l + b)}} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf{= 2(80 + 60)} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf{ = 160 + 120} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: { = \boxed{ \tt{ \pmb{ \purple{280 \: m}}}}}$

‎

➜Finding the cost of fencing:

This calculation can be carried out by multiplying the perimeter of the field with the rate of fencing per metre.

$\longmapsto{ \sf{280 \times 80}} \\ \\ \longmapsto \underline{ \boxed{ \tt{\pmb{\red{Rs. \: 22,400}}}}}$

$\\ \therefore \underline { \sf{ \pmb{The \: cost \: of \: fencing \: the \: field \: is \: Rs. \: \frak{22,400}}.}}$

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