Question

the sides of a rectangular swiming pool are in the ration of 5:3 and the area of the pool is 735sq.cm the length of the pool is _____ .

Answer 1

❍ Let's Consider Length of Rectangular swimming pool be 5x .

And ,

• Breadth of Rectangular swimming pool is 3x .

$\underline {\frak{\dag As \:We \:know \:that \: : }}$

$\qquad \qquad \qquad \underline {\boxed {\sf{ \bigstar Area _{(Rectangle)} = l \times b \:sq.units}}}$

Where ,

• l is the Length of Rectangle in cm and b is the Breadth of Rectangle in cm and We have given with the Area of Rectangle is 735 cm² .

⠀⠀⠀⠀⠀⠀$\underline {\bf{\star\:Now \: By \: Substituting \: the \: Given \: Values \::}}$

$\qquad \qquad:\implies \sf{ 735 cm^{2} = 5x \times 3x }$

$\qquad \qquad:\implies \sf{ 735cm^{2} = 15x^{2} }$

$\qquad \qquad:\implies \sf{ \dfrac{\cancel {735}}{\cancel {15}} = x^{2} }$

$\qquad \qquad:\implies \sf{ 49 = x^{2} }$

$\qquad \qquad:\implies \sf{ \sqrt{49} = x }$

⠀⠀⠀⠀⠀$\underline {\boxed{\pink{ \mathrm {  x = 7\: cm}}}}\:\bf{\bigstar}$

Therefore,

• Length of Rectangle is 5x = 5 × 7 = 35 cm .

• Breadth of Rectangle is 3x = 3×7 = 21 cm .

Therefore,

⠀⠀⠀⠀⠀$\therefore{\underline{\mathrm {  Length \: \:of\:Rectangular \:swimming \:pool\:is\:\bf{35cm\:\:}\: \: . }}}$

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$\large {\boxed{\sf{\mid{\overline {\underline {\star Verification \::}}}\mid}}}$

$\underline {\frak{\dag As \:We \:know \:that \: : }}$

• $\qquad \qquad \qquad \underline {\boxed {\sf{ \bigstar Area _{(Rectangle)} = l \times b \:sq.units}}}$

Where ,

• l is the Length of Rectangle in cm and b is the Breadth of Rectangle in cm and We have given with the Perimeter of Rectangle is 735cm² .

⠀⠀⠀⠀⠀⠀$\underline {\bf{\star\:Now \: By \: Substituting \: the \: Given \: Values \::}}$

$\qquad \qquad:\implies \sf{ 735cm^{2} = 35 \times 21 )}$

⠀⠀⠀⠀⠀$\underline {\boxed{\pink{ \mathrm {  735cm^{2} = 735\: cm^{2}}}}}\:\bf{\bigstar}$

⠀⠀⠀⠀⠀$\therefore \bf{\underline { Hence \:Verified \:}}$

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Diagram :

$\setlength{\unitlength}{1cm}\begin{picture}(0,0)\thicklines\multiput(0,0)(5,0){2}{\line(0,1){3}}\multiput(0,0)(0,3){2}{\line(1,0){5}}\put(0.03,0.02){\framebox(0.25,0.25)}\put(0.03,2.75){\framebox(0.25,0.25)}\put(4.74,2.75){\framebox(0.25,0.25)}\put(4.74,0.02){\framebox(0.25,0.25)}\multiput(2.1,-0.7)(0,4.2){2}{\sf\large 35\: cm}\multiput(-1.4,1.4)(6.8,0){2}{\sf\large 21\: cm}\put(-0.5,-0.4){\bf A}\put(-0.5,3.2){\bf D}\put(5.3,-0.4){\bf B}\put(5.3,3.2){\bf C}\end{picture}$

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$\large {\boxed{\sf{\mid{\overline {\underline {\star More\:To\:know\::}}}\mid}}}$

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

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Note : Kindly view this Answer in web :)

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Answer 2

Given: Ratio of length and breadth of a rectangular pool is 5:3. & Area of pool is 735 cm².

Need to find: Dimensions of rectangular pool?

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❍ Let's consider length and breadth of rectangular park be 5x and 3x.

⠀⠀⠀⠀⠀

As we know that,

⠀⠀⠀⠀⠀

$\begin{gathered}\star\:{\underline{\boxed{\frak{Area_{\:(rectangle)} = Length \times Breadth}}}}\\\\\\ \bf{\dag}\:{\underline{\frak{Putting\:given\:values\:in\:formula,}}}\\\\\\ :\implies\sf 735= 5x \times 3x\\\\\\ :\implies\sf 735 = 15x^2\\\\\\ :\implies\sf x^2 = \cancel{\dfrac{735}{15}}\\\\\\ :\implies\sf x^2 = 144\\\\\\ :\implies\sf \sqrt{x^2} = \sqrt{49} \\\\\\ :\implies{\underline{\boxed{\frak{\purple{x = 7}}}}}\:\bigstar\\\\\end{gathered}$

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Therefore,

⠀⠀⠀⠀⠀

Length of rectangular pool, 5x = 35cm

Breadth of rectangular pool, 3x = 21cm

⠀⠀⠀⠀⠀

$\therefore\:{\underline{\sf{Hence,\:Dimensions\:of\:rectangular\:pool\:is\:\bf{35\:cm}\: \sf{and}\: \bf{21\:m}\: \sf{respectively}.}}}$