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 th

Question

Vesna [10]

2 years ago

12

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 th

e breadth of the pool?

Mathematics

2 answers:

const2013 [10] · Answer 1 · 2023-01-17T07:19:19+03:00

const2013 [10]2 years ago

4 0

Step by step:

Perimeter = Summation of all sides = AB+BC+CD+DA = 2x+2+x+2x+2+x=(6x+4)

⇒6x+4=154

⇒6x=154−4

⇒ $\frac{150}{6x}$

⇒25=x

The breadth is x=25

The length of the rectangular pool = (2×25+2)=50+2=52m

<em>breadth </em>is 25 and the<em> length </em>is 52

Hope it helps!

Zinaida [17] · Answer 2 · 2023-01-17T09:11:16+03:00

$\blue\star \rm\pink{ Question:}$

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?

$\\ \\$

$\blue\star \rm\pink{ Given :}$

Perimeter of swimming pool is 154 m
Length is 2m more than breadth

$\\ \\$

$\blue\star \rm\pink{ To ~Find :}$

Length of rectangular pool
Breadth of rectanglur pool

$\\ \\$

$\blue\star \rm\pink{Let :}$

Breadth of x
Length be (2 + 2x)

$\\ \\$

We know:-

$\bigstar \boxed{ \rm perimeter \: of \: rextangle = 2(length +breadth)}$

So:-

$\\ \\$

$\dashrightarrow\sf perimeter \: of \: rextangle = 2(length +breadth) \\$

$\\ \\$

$\dashrightarrow\sf 154 = 2( 2 + 2x +x) \\$

$\\ \\$

$\dashrightarrow\sf 154 = 2( 2 + 3x) \\$

$\\ \\$

$\dashrightarrow\sf 154 = 2( 2 )+ 2(3x) \\$

$\\ \\$

$\dashrightarrow\sf 154 = 4+ 2(3x) \\$

$\\ \\$

$\dashrightarrow\sf 154 = 4+ 6x$

$\\ \\$

$\dashrightarrow\sf 154 - 4 =6x$

$\\ \\$

$\dashrightarrow\sf 150 =6x$

$\\ \\$

$\dashrightarrow\sf 6x = 150$

$\\ \\$

$\dashrightarrow\sf x = \dfrac{150}{6}$

$\\ \\$

$\dashrightarrow\sf x = \cancel \dfrac{150}{6}$

$\\ \\$

$\dashrightarrow\bf x =25$

$\\ \\$

Let's Verify value of x:-

$\\ \\$

$\dashrightarrow\sf 154 = 2( 2 + 2x +x) \\$

put value of x in equation

$\\ \\$

$\dashrightarrow\sf 154 = 2( 2 + \{2 \times 25 \} +25) \\$

$\\ \\$

$\dashrightarrow\sf 154 = 2( 2 + 50+25) \\$

$\\ \\$

$\dashrightarrow\sf 154 = 2( 2 + 75) \\$

$\\ \\$

$\dashrightarrow\sf 154 = 2(77) \\$

$\\ \\$

$\dashrightarrow\bf 154 =154$

$\\ \\$

$\Large \bf\dag LHS = RHS \dag$

Hence proved

$\\ \\$

Finally Let's find length and breadth of pool:-

$\\ \\$

To find breadth

➙ Breadth = x

➙ Breadth = 25 m

$\\$

To find length

➙ Length = 2 + 2x

➙ Length = 2 + 2(25)

➙ Length = 2 + 50

➙ Length = 52 m

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Cheers! all done. :)