Question

3. The length and breadth of a rectangular field are in the
ratio 3:2. If the area of the field is 3456m2, find the
cost of fencing it at Rs 60 per metre.​

Answer 1

Answer:

length and breadth of rectangular field is 3x:2x

area of rectangle =l×b

3456=3x×2x

3456=6x^2

3456/6=x^2

576=x^2 3

x=24

so,the length is72

breadth is 48

perimeter =2(l+b)

=2(72+48)

=240m

cost of fencing 1m = Rs 60

cost of fencing 240 m=240×60

= 14400

Answer 2

Answer :-

• The cost of fencing the rectangular field is Rs 14400.

Given :-

• The length and breadth of a rectangular field are in the ratio 3 : 2.

• The area of the field is 3456 m².

To find :-

• The cost of fencing it at the rate of Rs 60 per metre.

Step-by-step explanation :-

• Let's find the cost of fencing the rectangular field step-by-step!

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Finding the dimensions of the rectangular field :-

• Since the length and breadth of a rectangular field are in the ratio 2 : 3, therefore let them be 2x and 3x respectively.

It has been given that :-

• The area of the field is 3456 m².

We know that :-

$\underline{ \boxed{ \sf Area  \: of \:  a  \: rectangle = Length \times Breadth}}$

Here,

• Length = 2x.

• Breadth = 3x.

Substituting the given values in this formula,

$\hookrightarrow \rm2x \times 3x = 3456$

Multiplying 2x with 3x,

$\hookrightarrow \rm6{x}^{2}  = 3456$

Transposing 6 from LHS to RHS, changing it's sign,

$\hookrightarrow \rm {x}^{2}  =  \dfrac{3456}{6}$

Dividing 3456 by 6,

$\hookrightarrow \rm {x}^{2}  = 576$

Now let's find the square root of 576.

$\hookrightarrow\rm x =  \sqrt{576}$

Finding the square root,

$\hookrightarrow\overline{ \boxed{\rm x = 24 \: m}}$

Hence, the dimensions are :-

$\bf Length = 2x = 2 \times 24 = 48  \: m.$

$\bf Breadth = 3x = 3 \times 24 = 72 \: m.$

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Finding the perimeter of the field :-

• Now let's find the perimeter of the field using the dimensions!

• We have to find the perimeter of the rectangular field since we are asked to fence it.

We know that :-

$\underline{ \boxed{ \sf Perimeter  \: of \:  a \:  rectangle = 2  \: (L + B)}}$

Here,

• Length = 48 m.

• Breadth = 72 m.

Hence,

$\leadsto\rm Perimeter = 2 \: (48 + 72)$

Adding the numbers inside the brackets,

$\leadsto \rm Perimeter = 2 \: (120)$

Removing the brackets,

$\leadsto \rm Perimeter = 2 \times 120$

Multiplying 2 with 120,

$\leadsto\overline{\boxed{\rm Perimeter = 240 \: m.}}$

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Finding the cost of fencing the field :-

• The cost of fencing 1 metre = Rs 60.

• Hence, the cost of fencing 240 m is :-

$\longmapsto\overline{\boxed{\bf 240 \times 60 = Rs \: 14400}}$

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