Question

the length and breadth of a rectangular feild are in the ratio 5:3. The area of the feild is 3375m^2, find the cost of fencing the feild at rs5/m​

Answer 1

Answer:

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Answer 2

$\large{\underbrace{\underline{\bf{Required\:Answer:-}}}}$

$\frak{Given}\begin{cases}\sf{Length:Breadth=\bf{5:3.}}\\\sf{Area\:of\:the\:Field=\bf{3375\:m^2.}}\\\sf{Rate\:of\:fencing=\bf{Rs\:5\:per\:m.}}\end{cases}$

$\underline{\bf{\bigstar\:To\:Find:-}}$

• The cost of fencing the field.

$\underline{\bigstar\bf\:Solution:-}$

» Using the given ratio of sides and the area of the field, we would find the sides of the field.

» After finding the sides, using the formula of perimeter of a rectangle, we would find the perimeter of the field.

» Then, using the perimeter and the given rate , we would find the final answer i.e. the Cost of fencing.

◆ Finding the Sides of the field ◆

We know,

• Length : Breadth = 5:3

Let the ratios be 5x and 3x .

It means -

• Length = 5x
• Breadth = 3x

Using the formula of Area -

$\odot\;\boxed{\sf Area _{\:Rectangle}=Length\times Breadth}$

Put the values..

$\colon \rarr \sf \: \cancel {3375} \: {m}^{2} = \cancel5x \times 3x \\ \\ \colon \rarr \sf \: \cancel{675} \: {m}^{2} = \cancel3 \: {x}^{2} \\ \\ \colon \rarr \sf \: {x}^{2} = 225 \: {m}^{2} \\ \\ \colon \rarr \sf \: x = \sqrt{225 \: {m}^{2} } \\ \\ \colon \dashrightarrow \boxed{ \bf{ \pink{x = 15 \: m}}}$

So,

$\colon \leadsto\sf \: length = 5x = 5 \times 15 \: m \\ \\ \colon \dashrightarrow \boxed{ \boxed{ \bf{ \purple{length = 75 \: m}}}}$

And,

$\colon \leadsto \sf \: breadth = 3x = 3 \times 15 \: m \\ \\ \colon \dashrightarrow \boxed{ \boxed{ \bf{ \red{breadth = 45 \: m}}}}$

◆ Finding the Cost of fencing ◆

We have :

• Length = 75 m
• Breadth = 45 m

Using the formula for finding Perimeter..

$\odot\:\boxed{\sf Perimeter_{\:Rectangle} = 2(Length+Breadth)}$

Put the values..

$\colon \rarr \sf \: perimeter = 2(75 + 45) \: m \\ \\ \colon \rarr \sf \: perimeter = 2 \times 120 \: m \\ \\ \colon \dashrightarrow \boxed{ \bf{ \pink{perimeter = 240 \: m}}}$

Now,

We know :

• Rate of fencing = Rs 5 per m.

As,

$\sf \colon \leadsto \: cost = rate \times perimeter$

so,

$\colon \rarr \sf \: cost = 5 \times 240 \: rs \\ \\ \colon \dashrightarrow \boxed{ \boxed{ \frak{ \red{cost = 1200 \: rs}}}}$

$\therefore\;\underline{\sf Cost\:of\:Fencing\:the\:field=\bf{1200\:Rs.}}$

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