Question

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

Answer 1

Given :

• The perimeter of a rectangular swimming pool is 154 meters.
• Its length is 2m more than twice its breadth.

To find :

• The length and the breadth of the pool =?

Step-by-step explanation :

Let the breadth of the rectangular swimming pool be x.

Then, the length of the rectangular swimming pool be, 2 + 2x.

As We know that,

Perimeter of the rectangle = 2(length + breadth)

Substituting the values in the above formula, we get,

2(2 + 2x + x) = 154

2(2 + 3x) = 154

4 + 6x = 154

6x = 154 - 4

6x = 150

x = 150/6

x = 25

Hence, We get the value of x = 25 m.

Therefore, Breadth of the rectangular swimming pool, x = 25 m.

Length of the rectangular swimming pool, 2 + 2x = 52 m.

Answer 2

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

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:-

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

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

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

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

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