Question

Varma has an orchard of length and breadth 280 m

and 200 m respectively. He wants to fence it with barbed

wire. Find the cost of fencing at ₹35 per metre.

Answer 1

${ \large{ \red{ \underline{ \pmb{ \frak{Given...}}}}}}$

➼ Varma has an orchard of length and breadth 280 m and 200 m respectively.

➼ The cost of fencing the field is ₹35 per metre.

${ \large{ \red{ \underline{ \pmb{ \frak{To \: find...}}}}}}$

➼ The cost of fencing the rectangular field.

${ \large{ \red{ \underline{ \pmb{ \frak{Understanding \: the \: concept ...}}}}}}$

★ Now, we have the length and the breadth of the field and we have to find the cost of fencing it. we know that we fence the border of the field. here, the length of the border is nothing but It perimeter of the field. so, let's find the perimeter of the field in terms of the unit meters and then multiply it with the cost of fencing per meter.

${ \large{ \red{ \underline{ \pmb{ \frak{Solution ...}}}}}}$

➱ The cost to fence the orchard is ₹33600

${ \large{ \red{ \underline{ \pmb{ \frak{Calculations...}}}}}}$

★We know that,

$\: \: \: \: \: \: \: \dag \: \bigg( \bf \: perimeter_{(rectangle)} =2 (lenght + breadth \bigg)$

★ Here,

• Length = 280m
• Breath = 200m

★ Substituting we get,

${ : \implies} \sf \: perimeter_{(recangle)} = 2(l + b) \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ { : \implies} \sf \: perimeter_{(recangle)} = 2(280 + 200) \\ \\ \\ { : \implies} \sf \: perimeter_{(recangle)} = 2(480) \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ { : \implies} \sf \: perimeter_{(recangle)} = { \pink{ \underline{ \boxed{ \frak{ 960m}}} \star}} \: \: \: \: \: \: \: \:$

• Henceforth the perimeter of the orchard is 960m

★ Now,

• Let's find the cost to fence it

★ We know,

• Cost of fencing it is ₹ 35 per meter

★ So,

${ : \implies} \sf \: cost_{(fencing)} = perimeter \times 35 \\ \\ \\ { : \implies} \sf \: cost_{(fencing)} = 960 \times 35 \: \: \: \: \: \: \: \: \: \: \\ \\ \\ { : \implies} \sf \: cost_{(fencing)} = {\pink{ \underline{ \boxed{ \pmb{ \frak{Rs.33600}}}} \star}} \: \: \:$

• So, the cost = ₹33600

${ \large{ \red{ \underline{ \pmb{ \frak{Therefore...}}}}}}$

★ The cost to fence the orchard is rupees 33600

${ \large{ \red{ \underline{ \pmb{ \frak{Diagram...}}}}}}$

❍ Rectangle :

$\setlength{\unitlength}{1cm}\begin{picture}(0,0)\thicklines\multiput(0,0)(5,0){2}{\line(0,1){3}}\multiput(0,0)(0,3){2}{\line(1,0){5}}\multiput(2.1,-0.7)(0,4.2){2}{\sf\large 280 cm}\multiput(-1.4,1.4)(6.8,0){2}{\sf\large 200 cm}\end{picture}$

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