Question

The perimeter of a rectangular swimming pool is 154m. Its length is 2m more than twice its breadth. Find the length and the breadth of the pool ?

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Answer 1

Given : The perimeter of a rectangular swimming pool is 154m & Its length is 2m more than twice its breadth.

To Find : Find the length and the breadth of the pool ?

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Solution : Here, we have given that the perimeter of the swimming pool is 154m and the length of the swimming pool is 2m more than twice of the breadth of the pool.

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$\underline{\frak{As ~we ~know ~that~:}}$

• $\boxed{\sf\pink{Perimeter~ of ~rectangle~=~2\bigg(l~+~b\bigg)}}$

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Now,

• Let the Breadth of the pool be xm
• The length is 2m more that twice the breadth
• Length of the pool is 2x + 2m

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

$~~~\begin{gathered} \bf52m \: \: \: \: \: \: \: \: \: \: \: \\ \begin{gathered}\begin{gathered}\boxed{\begin{array}{}\bf { \red{}}\\{\qquad \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: }{}\\ { \sf{ }}\\ { \sf{ }} \\ \\ { \sf{ }}\end{array}}\end{gathered}\end{gathered} \bf25m\end{gathered}$

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So,

• let's substitute the values now and simply the equation so that we will find the dimensions of the pool.

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$\qquad\qquad{\sf:\implies{ perimeter ~= ~2\bigg(l ~+~ b\bigg)}}$

$\qquad\qquad{\sf:\implies {154m~ = ~2\bigg(x~ + ~2x ~+ ~2\bigg)}}$

$\qquad\qquad{\sf:\implies{154m ~= ~2\bigg(3x ~+ ~2\bigg)}}$

$\qquad\qquad{\sf:\implies{154m~ =~ 6x ~+ ~4}}$

$\qquad\qquad{\sf:\implies{6x~ = ~154~ -~ 4}}$

$\qquad\qquad{\sf:\implies{6x~ = 150}}$

$\qquad\qquad{\sf:\implies{x~ = ~\cancel\dfrac{150}{6}}}$

$\qquad\qquad:\implies{\underline{\boxed{\frak{\purple{x~=~25m}}}}}$★

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Now,

❍ Let's find the dimensions,

• Length of the pool = 2x + 2 = 52m
• Breadth of the pool = x = 25m

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Hence,

$\therefore\underline{\sf{The~ dimensions ~are ~\bf{\underline{52m}}~ \sf{and}~\bf{\underline{25m}}}}$

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$\pmb{\frak{\underline{More ~Information~:}}}$

• ${\sf\leadsto{Area~ of ~a ~rectangle~ =~ length~ × ~breadth}}$

• ${\sf\leadsto{Area ~of~ a ~square ~=~ side~ ×~ side}}$

• ${\sf\leadsto{Area~ of ~a ~triangle ~= ~\dfrac{1}{2}~ ×~ base~ × ~height}}$

• ${\sf\leadsto{Area ~of~ a~ rhombus~ =~\dfrac{d_{1}~×~d_{2}}{2}}}$

• ${\sf\leadsto{Area ~of ~a ~parallelogram~ = ~base~ ×~ height}}$

• ${\sf\leadsto{Perimeter ~of ~square~ = ~4 ~×~ side}}$

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Answer 2

Answer:

length of the pool =2x + 2 =2 x 25+ 2= 50+ 2 = 52m and breadth of the pool = 25 m