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?
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The perimeter of a rectangular swimming pool is 154 meters. Its length is 2m more than twice its breadth. What are
Verified answer
Given :
To Find :
Solution :
[tex]\longmapsto\tt{Let\:Breadth\:be=x}[/tex]
As Given that Length is 2m more than twice its breadth. So ,
[tex]\longmapsto\tt{Length=2x+2}[/tex]
Using Formula :
[tex]\longmapsto\tt\boxed{Perimeter\:of\:Rectangle=2(l+b)}[/tex]
Putting Values :
[tex]\longmapsto\tt{154=2(2x+2+x)}[/tex]
[tex]\longmapsto\tt{\cancel\dfrac{154}{2}=3x+2}[/tex]
[tex]\longmapsto\tt{77-2=3x}[/tex]
[tex]\longmapsto\tt{75=3x}[/tex]
[tex]\longmapsto\tt{x=\cancel\dfrac{75}{3}}[/tex]
[tex]\longmapsto\tt\bf{x=25}[/tex]
Value of x is 25 .
Therefore :
[tex]\longmapsto\tt{Length\:of\:Pool=2(25)+2}[/tex]
[tex]\longmapsto\tt\bf{52\:m}[/tex]
[tex]\longmapsto\tt{Breadth\:of\:Pool=x}[/tex]
[tex]\longmapsto\tt\bf{25\:m}[/tex]
Answer:
Breadth = 25 m
Length = 52 m
Step-by-step explanation:
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.
Solution:-
[tex] \rm \: Let \: breadth \: be \: x \: m \\ \therefore \rm\: length = 2x + 2 \: m \\ [/tex]
♠ Formula Used-
[tex] \boxed{ \green{ \rm \: Perimeter \: of \: pool = 2( \: length + breadth)}}[/tex]
Now,
ACQ,
[tex] \therefore \rm \: 2(2x + 2 + x) = 154 \\ \rm : \longmapsto \: 2(3x + 2) = 154 \\ \rm : \longmapsto \: 3x + 2 = \cancel \frac{154}{2} \\ \rm : \longmapsto \: 3x + 2 = 77 \\ \rm : \longmapsto \: 3x = 77 - 2 \\ \rm : \longmapsto \: 3x = 75 \\ \rm : \longmapsto \: x = \cancel\frac{75}{3} \\ \rm : \longmapsto \: x = 25[/tex]
So,
Breadth = 25 m
Length = 2x + 2
= 2(25)+2
= 50 + 2
= 52 m