Question

The area of a square plot is 60025m2
. Find the cost of fencing the plot at
the rate of Rs.50 per metre

Answer 1

Answer:

Rs 49000

Step-by-step explanation:

Area = 60025 m2

If Rs 50 pm then

Area of a square plot = 60025 m²

We know that,

Area of a square = a² where a is the side's length.

→ a² = 60025

→ a² = (245)²

→ a = 245 m

Length of side of the square plot = 245 m

We have to find:

The cost of fencing the plot at rate of Rs. 50 per m.

Cost of fencing the plot = 50 * perimeter of the plot.

Perimeter of a square = 4a

Hence,

Cost of fencing the plot = 50 * 4 * 245

→ Cost of fencing the plot = Rs. 49,000

Hence, it costs Rs. 49,000 to fence the plot.

Answer 2

Answer:

${\large{\underline{\underline{\pmb{\frak{Given:-}}}}}}$

• ★ Area of a square plot = 60025 m²
• ★ Cost of fencing the plot at the rate = 50 per meter

$\begin{gathered}\end{gathered}$

${\large{\underline{\underline{\pmb{\frak{To \: Find:-}}}}}}$

• ★ The cost of fencing the plot at rate of Rs. 50 per m.

$\begin{gathered}\end{gathered}$

${\large{\underline{\underline{\pmb{\frak{Using \: Formulae :-}}}}}}$

$\quad\bigstar{\underline{\boxed{\sf{Side \: of \: square = \sqrt{Area \: of \: square}}}}}$

$\quad\bigstar{\underline{\boxed{\sf{Perimeter \: of \: square = 4 × side }}}}$

$\quad{\bigstar{\underline{\boxed{\sf{Total \: Cost = Perimeter \: of \: Square \: plot \times Cost \: of \: fencing \: per \: meter}}}}}$

$\begin{gathered}\end{gathered}$

${\large{\underline{\underline{\pmb{\frak{Diagram:-}}}}}}$

$\setlength{\unitlength}{1cm}\begin{picture}(0,0)\thicklines\multiput(0,0)(4,0){2}{\line(0,1){4}}\multiput(0,0)(0,4){2}{\line(1,0){4}}\put(-0.5,-0.5){\bf D}\put(-0.5,4.2){\bf A}\put(4.2,-0.5){\bf C}\put(4.2,4.2){\bf B}\put(1.5,-0.6){\bf\large 245\ m}\put(4.4,2){\bf\large 245\ m}\end{picture}$

$\begin{gathered}\end{gathered}$

${\large{\underline{\underline{\pmb{\frak{Solution:-}}}}}}$

$\red\bigstar$ Firstly finding the side of square :-

$\quad{\dashrightarrow{\sf{Side \: of \: square = \sqrt{Area \: of \: square}}}}$

• Substuting the values

$\quad{\dashrightarrow{\sf{Side \: of \: square = \sqrt{60025 \: {m}^{2} }}}}$

$\quad{\dashrightarrow{\sf{Side \: of \: square = \sqrt{245 \times 245}}}}$

$\quad{\dashrightarrow{\sf{Side \: of \: square = {245 \: m}}}}$

$\quad{\bigstar{\underline{\boxed{\sf{\purple{Side \: of \: square = {245 \: m}}}}}}}$

∴ The side of square is 245 m.

$\begin{gathered}\end{gathered}$

$\red\bigstar$ Now, Finding the perimeter of square :-

$\quad{: \implies{\sf{Perimeter \: of \: square = 4 × side }}}$

• Substuting the values

$\quad{: \implies{\sf{Perimeter \: of \: square = 4 × 245}}}$

$\quad{: \implies{\sf{Perimeter \: of \: square = 980 \: m}}}$

$\quad{\bigstar{\underline{\boxed{\sf{\purple{Perimeter \: of \: square = 980 \: m}}}}}}$

∴ The Perimeter of square is 980 m.

$\begin{gathered}\end{gathered}$

$\red\bigstar$ Now, Calculating the total cost of fencing the plot :-

$\quad{: \longmapsto{\sf{Total \: Cost = Perimeter \: of \: Square \: plot \times Cost \: of \: fencing \: per \: meter}}}$

• Substuting the values

$\quad{: \longmapsto{\sf{Total \: Cost = 980\times 50}}}$

$\quad{: \longmapsto{\sf{Total \: Cost = Rs.49000}}}$

$\quad{\bigstar{\underline{\boxed{\sf{\purple{Total \: Cost = Rs.49000}}}}}}$

∴ The cost of fencing the plot at the rate of Rs.50 per metre is Rs.49000.

$\begin{gathered}\end{gathered}$

${\large{\underline{\underline{\pmb{\frak{Learn \: More:-}}}}}}$

$\boxed{\begin {minipage}{9cm}\\ \dag\quad \Large\underline{\bf Formulas\:of\:Areas:-}\\ \\ \star\sf Square=(side)^2\\ \\ \star\sf Rectangle=Length\times Breadth \\\\ \star\sf Triangle=\dfrac{1}{2}\times Breadth\times Height \\\\ \star \sf Scalene\triangle=\sqrt {s (s-a)(s-b)(s-c)}\\ \\ \star \sf Rhombus =\dfrac {1}{2}\times d_1\times d_2 \\\\ \star\sf Rhombus =\:\dfrac {1}{2}p\sqrt {4a^2-p^2}\\ \\ \star\sf Parallelogram =Breadth\times Height\\\\ \star\sf Trapezium =\dfrac {1}{2}(a+b)\times Height \\ \\ \star\sf Equilateral\:Triangle=\dfrac {\sqrt{3}}{4}(side)^2\end {minipage}}$

$\begin{gathered}\end{gathered}$

${\large{\underline{\underline{\pmb{\frak{Request:-}}}}}}$

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