Question

The perimeter of a rectangular swimming pool is 154 . It's length is 2m more than twice it's breadth . What are the length and the breadth of the pool .​

Answer 1

Given :

• Perimeter of rectangular swimming pool = 154 m
• Length is 2 m more than twice the breadth of the swimming pool

To find :

• Length and breadth of the pool

Concept :

Firstly, we will assume the breadth as any variable, let it be x and then length will be 2 m more than twice the breadth, i.e. 2x + 2. So, by using the formula of perimeter of rectangle. Find the value of x and after getting its value substitute it in the length and breadth of the swimming pool which we've assumed. The resultant values will be the required answer.

Perimeter of any figure is the sum of all its sides.

Mathematically,

★ Perimeter = Sum of all the sides

Rectangle has 4 sides in which 2 sides are equal to each other. So, the formula of perimeter of rectangle :-

• Perimeter of rectangle = 2(l + b)

where,

• l denotes the length
• b denotes the breadth

Solution :

Let,

• Breadth of the rectangular swimming pool = x metre
• Length of the rectangular swimming pool = 2x + 2 metre

$\\ \twoheadrightarrow \quad \rm Perimeter \ of \ swimming \ pool = 2(l + b)$

Substituting the given values,

$\\ \twoheadrightarrow \quad \sf 154 = 2(2x + 2+ x)$

Transposing 2 to the left hand side.

$\\ \twoheadrightarrow \quad \sf \dfrac{154}{2} = 2x + 2+ x$

$\\ \twoheadrightarrow \quad \sf \dfrac{\!\!\!\not154}{ \!\!\!\not2} = 2x + 2+ x$

$\\ \twoheadrightarrow \quad \sf 77 = 2x + 2+ x$

$\\ \twoheadrightarrow \quad \sf 77 = 3x + 2$

Transposing 2 to the left hand side and changing it's sign.

$\\ \twoheadrightarrow \quad \sf 77 - 2 = 3x$

$\\ \twoheadrightarrow \quad \sf 75 = 3x$

Transposing 3 to the left hand side.

$\\ \twoheadrightarrow \quad \sf \dfrac{75}{3} = x$

$\\ \twoheadrightarrow \quad \sf \dfrac{\!\!\!\not75}{\!\!\!\not3} = x$

$\\ \twoheadrightarrow \quad \sf 25 = x$

The value of x = 25

Substituting the value of x in he dimensions of rectangular swimming pool ::

↠ Breadth of the swimming pool = x = 25 m

↠ Length of the swimming pool = 2x + 2 = 2(25) + 2 = 50 + 2 = 52

↠ Length of the swimming pool = 52 m

Therefore,

• The length and breadth of the rectangular swimming pool is 25 m and 52 m respectively.

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VERIFICATION :

★ To verify the value of length and breadth of the swimming pool, calculate the perimeter if it will be equal to 154 m (as mentioned in the question) then the value of length and breadth is right.

↠ Perimeter of swimming pool = 2(l + b)

↠ Perimeter of the swimming pool = 2(25 + 52)

↠ Perimeter of the swimming pool = 2(77)

↠ Perimeter of the swimming pool = 154

Perimeter of the swimming pool = 154 m

Hence, verified.

Answer 2

$\begin{gathered}\frak{Given} = \begin{cases} &\sf{The\: perimeter\: of\: a\: rectangular\: swimming \:pool\: is\: 154\: m\:.} \\\\\\\\\\\ &\sf{The\:length \:is\: 2\:m\: more\: than\: twice\: its\: breadth.}\end{cases}\end{gathered}$

To find:-

$\qquad\sf{:\implies\:The\:Length\:of\:the\:pool\:.}$

$\qquad\sf{:\implies\:The\:Breadth\:of\:the\:pool\:.}$

Assume:-

$\qquad\sf{:\implies\:The\:Breadth\:of\:the\:rectangular\:swimming\:pool\:=\:x.}$

$\qquad\sf{:\implies\:The\:Length\:of\:the\:rectangular\:swimming\:pool\:=\:2\:+\:2x.}$

Solution:-

$\qquad\sf{:\implies\:The\:perimeter\:of\:_{(Rectangle)}\:=\:2\:(\:Length\:+\:Breadth\:).}$

$\qquad\sf{:\implies\:154\:=\:2\:(\:2\:+\:2x\:+x).}$

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

$\qquad\sf{:\implies\:\dfrac{154}{2}\:=\:2\:+3x}$

$\qquad\sf{:\implies\:77\:=\:2\:+\:3x}$

$\qquad\sf{:\implies\:77\:-\:2=\:3x}$

$\qquad\sf{:\implies\:75\:=\:3x}$

$\qquad\sf{:\implies\:x\:=\dfrac{75}{3}}$

$\qquad\sf{:\implies\:x\:=\:25}$

Breadth:-

$\qquad\sf{:\implies\:Breadth\:of\:the\:rectangular\:swimming\:pool\:=\:x\:}$

$\qquad\sf{:\implies\:Breadth\:of\:the\:rectangular\:swimming\:pool\:=\:25m\:}$

$\color{blue}{\underline{\sf{Therefore\:the\:Breadth\:of\:the\:rectangular\:swimming\:pool\:is\:25\:m\:.}}}$

Length:-

$\qquad\sf{:\implies\:Length\:of\:the\:rectangular\:swimming\:pool\:=\:2\:+\:2x}$

$\qquad\sf{:\implies\:Length\:of\:the\:rectangular\:swimming\:pool\:=\:2\:+\:2\:\times\:25}$

$\qquad\sf{:\implies\:Length\:of\:the\:rectangular\:swimming\:pool\:=\:2\:+\:50}$

$\qquad\sf{:\implies\:Length\:of\:the\:rectangular\:swimming\:pool\:=\:52m}$

$\color{lime}{\underline{\sf{Therefore\:the\:Length\:of\:the\:rectangular\:swimming\:pool\:is\:52\:m\:.}}}$