Question

Q6. The sides of a rectangular park are in the
ratio 4:3. If its area is 1728 m , find the
cost of fencing it at Rs. 2.50 per metre.​

Answer 1

Answer:

1728 = 4x×3x = 1728= square of 12x = x square is 1728 ÷ 12 =144 square root =12

therefore l= 48 m and b= 36m 2(48+36)2.50=420 therefore ₹420 is correct answer

Answer 2

⋆ DIAGRAM:

$\setlength{\unitlength}{0.9cm}\begin{picture}(0,0)\thicklines\multiput(0,0)(5,0){2}{\line(0,1){3}}\multiput(0,0)(0,3){2}{\line(1,0){5}}\put(0.03,0.02){\framebox(0.25,0.25)}\put(0.03,2.75){\framebox(0.25,0.25)}\put(4.74,2.75){\framebox(0.25,0.25)}\put(4.74,0.02){\framebox(0.25,0.25)}\multiput(2.1,-0.7)(0,4.2){2}{\sf\large }\multiput(-1.4,1.4)(6.8,0){2}{\sf\large }\put(-0.5,-0.4){\bf A}\put(-0.5,3.2){\bf D}\put(5.3,-0.4){\bf B}\put(5.3,3.2){\bf C}\end{picture}$

⠀⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━⠀⠀⠀⠀⠀⠀⠀

Given: ABCD is a rectangular park. And, the sides of a rectangular park are in the ratio of 4:3. Area of rectangular park is 1728 m².

Need to find: The cost of fencing.

Let the sides of the rectangular park are 4x and 3x respectively.

⠀⠀

⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━━━

⠀⠀

⋆ Area of Rectangle is given by,

$\star\;\boxed{\sf{\pink{Area_{\:(rectangle)} = Length \times Breadth}}}$

⠀

Therefore,

⠀

$:\implies\sf Area_{\:(park)} = Length \times Breadth \\\\\\:\implies\sf 1728 = 4x \times 3x \\\\\\:\implies\sf 1728 = 12x^2 \\\\\\:\implies\sf x^2 = \cancel\dfrac{1728}{12} \\\\\\:\implies\sf x^2 = 144 \\\\\\:\implies\sf x = \sqrt{144} \\\\\\:\implies{\underline{\boxed{\frak{\pink{x = 12}}}}}$

⠀⠀

$\underline{\bigstar\:\textsf{Sides of the rectangular park are :}}$

⠀⠀

• Length of the rectangular park, 4x = 4(12) = 48m

• Breadth of the rectangular park, 3x = 3(12) = 36m.

$\therefore{\underline{\sf{Hence,\;length \; and \; Breadth\; of \; park \; are \; \bf{48\:m}\;and\:\bf{36\;m}\; respectively.}}}$

⠀⠀

⠀⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━⠀⠀⠀⠀⠀⠀⠀⠀

To calculate the cost of fencing the rectangular park, we've to find out the perimeter of the rectangular park.

As we know that, perimeter of the rectangle is given by :

$\star\;\boxed{\sf{\purple{Perimeter_{\:(rectangle)} = 2\Big\lgroup Length + Breadth \Big\rgroup}}}$

⠀⠀⠀

$\underline{\bf{\dag} \:\mathfrak{Putting\:values\: :}}$⠀⠀⠀

⠀⠀

$\leadsto\sf Perimeter_{\:(park)} = 2 \Big\lgroup Length + Breadth \Big\rgroup \\\\\\\leadsto\sf Perimeter_{\:(park)} = 2 \Big\lgroup 48 + 36 \Big\rgroup \\\\\\\leadsto \sf Perimeter_{\:(park)} = 2 \times 84 \\\\\\\leadsto{\underline{\boxed{\frak{Perimeter_{\:(park)} = 168\;m}}}}$

⠀⠀

$\therefore{\underline{\sf{Hence, perimeter \;of\; park\;is\; \bf{168\;m }.}}}$

⠀⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━⠀⠀⠀⠀⠀⠀⠀⠀

❍ Now, finding the cost of fencing the rectangular park at Rs. 2.50 per m.

⠀⠀

Therefore,

⠀

$\longrightarrow\sf Cost = Perimeter \times 2.50 \\\\\\\longrightarrow\sf Cost = 168 \times 2.50 \\\\\\\longrightarrow{\underline{\boxed{\frak{\purple{Cost = 420\;rs}}}}}\:\bigstar$

⠀⠀

$\therefore{\underline{\sf{Hence,\; required\; cost\:of\; fencing\;it\;is\; \bf{420\;rs }.}}}$