Question

The perimeter of a rectangular park is 200 m. If its breadth is 35 m, then find its length. Also, find the cost of growing grass at 12.50 per m square.​

Answer 1

Answer:

Given :

• ➝ Perimeter of rectangular park == 200 m.
• ➝ Breadth of rectangular park = 35 m.

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

To Find :

• ➝ Length of rectangular park
• ➝ The cost growing grass at 12.50 per m².

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Using Formulas :

• ➝ Perimeter of rectangle = 2(l + b)
• ➝ Area of rectangle = l × b
• ➝ Total cost = Area × Cost of growing grass per m².

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Solution :

Finding the length of rectangular park by substituting the values in the formula :

$\begin{gathered} \quad\quad{\longrightarrow{\sf{Perimeter = 2(l + b)}}}\\\\\qquad{\longrightarrow{\sf{200= 2(l + 35)}}}\\\\\qquad{\longrightarrow{\sf{\dfrac{200}{2} = (l + 35)}}}\\\\\qquad{\longrightarrow{\sf{\cancel{\dfrac{200}{2}} = (l + 35)}}}\\\\\qquad{\longrightarrow{\sf{100= (l + 35)}}}\\\\\qquad{\longrightarrow{\sf{ l = 100 - 35}}}\\\\ \qquad{\longrightarrow{\sf{ l = 65 \: m}}}\\\\\qquad\bigstar \: \underline{\boxed{\sf{\pink{Length = 65 \: m}}}}\end{gathered}$

Hence, the length of rectangular park is 65 m.

$\rule{300}{1.5}$

Finding the area of rectangular park by substituting the values in the formula :

$\begin{gathered} \quad\qquad{\dashrightarrow{\sf{Area = l \times b }}} \\ \\ \quad\qquad{\dashrightarrow{\sf{Area = 65\times 35}}} \\ \\ \quad\qquad{\dashrightarrow{\sf{Area = 2275 \: {m}^{2}}}} \\ \\ \quad\qquad\bigstar \: \underline{\boxed{\sf{\pink{Area = 2275 \: {m}^{2}}}}}\end{gathered}$

Hence, the area of rectangular park is 2275 m².

$\rule{300}{1.5}$

Now, finding the total cost of growing grass at 12.50 per m².

$\begin{gathered}{\implies{\sf{ Total \: cost = Area \times Cost \: of\: grass \: per \: {m}^{2}}}}\\\\{\implies{\sf{ Total \: cost = 2275 \times 12.50}}}\\\\{\implies{\sf{ Total \: cost = 2275 \times \dfrac{1250}{100}}}}\\\\{\implies{\sf{ Total \: cost = 2275 \times \dfrac{125\cancel{0}}{10 \cancel{0}}}}}\\\\{\implies{\sf{ Total \: cost = 2275 \times \dfrac{125}{10}}}}\\\\{\implies{\sf{ Total \: cost = \dfrac{2275 \times 125}{10}}}}\\\\{\implies{\sf{ Total \: cost = \dfrac{284375}{10}}}}\\\\{\implies{\sf{ Total \: cost = \cancel{\dfrac{284375}{10}}}}}\\\\{\implies{\sf{ Total \: cost = Rs.28437.5}}}\\\\ \bigstar\underline{\boxed{\sf{\pink{ Total \: cost = Rs.28437.5}}}}\end{gathered}$

Hence, the cost of growing grass is Rs.28437.5.

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

Learn More :

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

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