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Question => The perimeter of a rectangular swimming pool is 154 m. its length is 2 m more than twice its breadth. what are the length and the breadth of the pool?

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Answer 1

Given :

• The Perimeter of a rectangular swimming pool is 154 m.
• Length is 2 m more than twice its breadth.

To Find :

• Length and Breadth of the pool .

Solution :

$\longmapsto\tt{Let\:breadth\:be=x}$

As Given that length is 2 m more than twice its breadth. So ,

$\longmapsto\tt{Length=2x+2}$

Using Formula :

$\longmapsto\tt\boxed{Perimeter\:of\:Rectangle=2(l+b)}$

Putting Values :

$\longmapsto\tt{154=2(2x+2+x)}$

$\longmapsto\tt{\cancel\dfrac{154}{2}=3x+2}$

$\longmapsto\tt{77-2=3x}$

$\longmapsto\tt{75=3x}$

$\longmapsto\tt{x=\cancel\dfrac{75}{3}}$

$\purple\longmapsto\:\large\underline{\boxed{\bf\blue{x}\pink{=}\red{25}}}$

Therefore :

$\longmapsto\tt{Length\:of\:pool=2(25)+2}$

$\longmapsto\tt\bf{52\:m}$

$\longmapsto\tt{Breadth\:of\:pool=x}$

$\longmapsto\tt\bf{25\:m}$

Answer 2

$\bf{\dag}\:{\underline{\underline{\sf{Question\::}}}}$

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

$\bf{\dag}\:{\underline{\underline{\sf{Answer\::}}}}$

• Length of pool = 52 m

• Breadth of pool = 25 m

$\bf{\dag}\:{\underline{\underline{\sf{Given\::}}}}$

• Perimeter of rectangular swimming pool = 154 m
• It's length is 2 m more than twice it's breadth

$\bf{\dag}\:{\underline{\underline{\sf{To\:Find\::}}}}$

• Length and breadth of the pool?

$\bf{\dag}\:{\underline{\underline{\sf{Solution\::}}}}$

• Let breadth of pool be y m
• As it is given that it's length is 2 m more than twice it's breadth. So, length of pool is (2y + 2) m

$\bf{\dag}\:{\underline{\underline{\sf{Using\:Formula::}}}}$

$\quad\bigstar\:{\boxed{\sf{\pink{Perimeter_{(rectangle)} = 2(L + B)}}}}$

Where,

• L denotes length of rectangle
• B denotes breadth of rectangle

We have,

• L = length of pool = (2y + 2) m
• B = breadth of pool = y m
• Perimeter of pool = 154 m

$\underline{\bm{\bigstar\:Putting\:all\:values\::}}$

$\\ :\implies\:\tt 154 = 2\big[(2y + 2) + y\big]$

$\\ :\implies\:\tt 154 = 2(2y + 2 + y)$

$\\ :\implies\:\tt 154 = 2(2y + y + 2)$

$\\ :\implies\:\tt 154 = 2(3y + 2)$

$\\ :\implies\:\tt {\cancel{\dfrac{154}{2}}} = 3y + 2$

$\\ :\implies\:\tt 77 = 3y + 2$

$\\ :\implies\:\tt 3y + 2 = 77$

$\\ :\implies\:\tt 3y = 77 - 2$

$\\ :\implies\:\tt 3y = 75$

$\\ :\implies\:\tt y = {\cancel{\dfrac{75}{3}}}$

$\\ \pink{:\implies}\:{\purple{\underline{\underline{\boxed{\bf{\blue{y} \orange{=} \red{25}}}}}}}$

So,

• ➬ Length of pool = (2y + 2)

• ➬ Length of pool = (2 × 25) + 2

• ➬ Length of pool = 50 + 2

• ➬ Length of pool = 52 m

Also,

• ➬ Breadth of pool = y

• ➬ Breadth of pool = 25 m

Verification:

➻ Perimeter of pool = 154

➻ 2(L + B) = 154

➻ 2(52 + 25) = 154

➻ 2(77) = 154

➻ 2 × 77 = 154

➻ 154 = 154

➻ LHS = RHS

• Hence, Verified ✔

Know more:

• Perimeter of any figure is calculated by sum of its all sides.

• Perimeter of rectangle = 2(L + B)

• Perimeter of square = 4 × side

• Perimeter of circle = 2πr

• Perimeter of rhombus = 4 × side

• Perimeter of equilateral ∆ = 3 × side

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