Question

The length and the breadth of a rectangular park are in the ratio 5 : 3 and its perimeter is 128 m. Find the area of the park.​

Answer 1

Step-by-step explanation:

Let the length be 5x

and breadth be 3x

so, perimeter =2(l+b)

=2(5x+3x)

=2×7x

=14x

but here,perimeter is =14x=128

=x=128/14=64/7

so ,length =5×64/7=320/7m

breadth =3×64/7=192/7m

area of the park =l×b

=320/7×192/7

=61440/49

=1253.8775510204m^2

Answer 2

Answer:

${\large{\underline{\underline{\bf{Given \: : - }}}}}$

• $\twoheadrightarrow$ The length and the breadth of a rectangular park are in the ratio = 5 : 3.
• $\twoheadrightarrow$ Perimeter of rectangle = 128 m.

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

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

• $\twoheadrightarrow$ Area of rectangular park

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

${\large{\underline{\underline{\bf{Using \: Formulae\: : - }}}}}$

$\bigstar{\red{\underline{\boxed{\sf{Perimeter \: of \: Rectangle = 2(Lenght+ breadth)}}}}}$

$\bigstar{\red{\underline{\boxed{\sf{Area \: of \: Rectangle = Length \times Breadth }}}}}$

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

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

$\green\bigstar$ Let the,

• $\twoheadrightarrow$ Lenght of rectangle = 5x
• $\twoheadrightarrow$ Breadth of rectangle = 3x

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

$\green\bigstar$ Now, According to the question

${\dashrightarrow{\sf{Perimeter_{(Rectangle)} = 2(Lenght+ breadth)}}}$

• Substuting the values

${\dashrightarrow{\sf{128 \: m= 2(5x + 3x)}}}$

${\dashrightarrow{\sf{128 \: m= 2(8x)}}}$

${\dashrightarrow{\sf{128 \: m= 2 \times 8x}}}$

${\dashrightarrow{\sf{128 \: m= 16x}}}$

${\dashrightarrow{\sf{x = \dfrac{128}{16}}}}$

${\dashrightarrow{\sf{x = \cancel{\dfrac{128}{16}}}}}$

${\dashrightarrow{\sf{x = 8 \: m}}}$

$\bigstar{\red{\underline{\boxed{\bf{x = 8 \: m}}}}}$

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

$\green\bigstar$ Thus,

• $\twoheadrightarrow$ Lenght of rectangle = 5×8 = 40 cm
• $\twoheadrightarrow$ Breadth of rectangle = 3×8 = 24 cm

∴ The lenght of rectangular park is 40 m and The breadth of rectangular park is 24 m.

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

$\green\bigstar$ Now, Calculating the area of rectangle

${\dashrightarrow{\sf{Area_{(Rectangle)} = Lenght \times breadth}}}$

• Substuting the values

${\dashrightarrow{\sf{Area_{(Rectangle)} = 40 \: m \times 24 \: m}}}$

${\dashrightarrow{\sf{Area_{(Rectangle)} = 960\: {m}^{2} }}}$

${\bigstar{\red{\underline{\boxed{\bf{Area \: of \: rectangle = 960\: {m}^{2}}}}}}}$

∴ Area of rectangular park is 960 m².

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

${\large{\underline{\underline{\bf{Diagram\: : - }}}}}$

$\setlength{\unitlength}{1cm}\begin{picture}(0,0)\thicklines\multiput(0,0)(5,0){2}{\line(0,1){3}}\multiput(0,0)(0,3){2}{\line(1,0){5}}\put(0.03,0.02){\framebox(0.25,0.25)}\put(0.03,2.75){\framebox(0.25,0.25)}\put(4.74,2.75){\framebox(0.25,0.25)}\put(4.74,0.02){\framebox(0.25,0.25)}\multiput(2.1,-0.7)(0,4.2){2}{\sf\large 40\ m}\multiput(-1.4,1.4)(6.8,0){2}{\sf\large 24\ m}\put(-0.5,-0.4){\bf}\put(-0.5,3.2){\bf}\put(5.3,-0.4){\bf}\put(5.3,3.2){\bf}\end{picture}$

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

${\large{\underline{\underline{\bf{Learn \: More\: : - }}}}}$

$\green\bigstar$ Formulas of area 

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

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

${\large{\underline{\underline{\bf{Request\: : - }}}}}$

• ⟶ Diagram of rectangular park is given in the attachment.
• ⟶ If there is any difficulty viewing this answer in app, kindly see this answer at website Brainly.in for clear steps and understanding.
• ⟶ Here is the question link : https://brainly.in/question/35171276

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