Question

the lenght of a rectangular feild is thrice it's breadth.if the area of the feild is 7 500 sq. m.find the cost of fencing the feild at the rate of rs .10/m​

Answer 1

$\large\underline{\sf{Given- }}$

• The length of a rectangular field is thrice it's breadth.

• Area of Rectangular field = 7500 square meter.

• Cost of fencing 1 meter is Rs 10

$\large\underline{\sf{To\:Find - }}$

• Cost of fencing rectangular feild at the rate of Rs 10 per meter.

$\begin{gathered}\Large{\bold{{\underline{Formula \: Used - }}}}  \end{gathered}$

$1. \: \: \: \boxed{ \sf \: Area_{(rectangle)} = Length \times Breadth}$

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

$\large\underline{\sf{Solution-}}$

Given that

• Length of a rectangle is thrice of it's Breadth.

So,

$\begin{gathered}\begin{gathered}\bf \: Let - \begin{cases} &\sf{Breadth = x \:} \\ &\sf{Length = 3x} \end{cases}\end{gathered}\end{gathered}$

Now,

• Its given that

$\rm :\longmapsto\:Area_{(rectangle)} = 7500 \: {m}^{2}$

$\rm :\longmapsto\:Length \times Breadth = 7500$

$\rm :\longmapsto\:3x \times x = 7500$

$\rm :\longmapsto\: {x}^{2} = 2500$

$\rm :\longmapsto\:x = \sqrt{2500}$

$\rm :\longmapsto\:x = \sqrt{5 \times 5 \times 10 \times 10}$

$\bf\implies \:x \: = \: 50 \: m$

So,

Dimensions of rectangular feild is

$\begin{gathered}\begin{gathered}\bf \: Dimensions- \begin{cases} &\sf{Breadth = x = 50 \: m \:} \\ &\sf{Length = 3x = 3 \times 50 = 150 \: m} \end{cases}\end{gathered}\end{gathered}$

Now, to find the fencing of the rectangular feild, we have to find the Perimeter of Rectangular feild.

So,

$\rm :\longmapsto\:Perimeter_{(rectangle)} = 2(Length + Breadth)$

$\rm :\longmapsto\:Perimeter_{(rectangle)} = 2(50 + 150)$

$\rm :\longmapsto\:Perimeter_{(rectangle)} = 2 \times 200$

$\rm :\longmapsto\:Perimeter_{(rectangle)} = 400 \: m$

Now,

$\rm :\longmapsto\:Cost \: of \: fencing \: 1 \: m \: = \: Rs \: 10$

$\rm :\longmapsto\:Cost \: of \: fencing \: 400 \: m\:=\: 400 \times 10 = Rs \: 4000$

Additional Information :-

$1. \: \: \: \boxed{ \sf \: Area_{(circle)} = \pi \: {r}^{2} }$

$2. \: \: \: \boxed{ \sf \: Perimeter_{(circle)} = 2\pi \: r}$

$3. \: \: \: \boxed{ \sf \: Area_{(square)} = {(side)}^{2} }$

$4. \: \: \: \boxed{ \sf \: Perimeter_{(square)} = 4 \times side}$

$5. \: \: \: \boxed{ \sf \: Perimeter_{(rhombus)} = 4 \times side}$

$6. \: \: \: \boxed{ \sf \: Area_{(rhombus)} = base \times altitude}$