Question

2. The length of a rectangular swimming pool is 5m more than two times it's breadth. Find the length and breadth of pool if its perimeter is 160 m.
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Answer 1

Given :-

The length of a rectangular = (2 × Breadth) + 2

Perimeter of the swimming pool = 160 m

To Find :-

The length of the swimming pool.

The breadth of the swimming pool.

Analysis :-

Take the length and breadth as variables accordingly.

Make an equation and solve to get the value of the variable.

Apply that value in length and breadth in order to get the length and breadth of the swimming pool.

Solution :-

We know that,

• l = Length
• b = Breadth
• p = Perimeter

Let the length and breadth be 2x + 2 and x respectively.

Given that,

Perimeter (p) = 160 m

Breadth (b) = x

Length (l) = 2x + 2

According to the question,

$\underline{\boxed{\sf Perimeter \ of \ a \ rectangle=2(Length+Breadth)}}$

Substituting their values, we get

Perimeter of the swimming pool = $\sf 2(2x+2+x)=160$

$\longrightarrow \sf 2(3x+2)=160$

$= \sf 3x+2=\dfrac{160}{2}$

$\sf =3x+2=80$

$\sf =3x=80-2$

$= \sf 3x=78$

$= \sf x=\dfrac{78}{3}$

$= \sf x=26$

Hence, the value of x is 26

Breadth = x = 26 cm

Length = $\sf 2x + 2$

$=\sf (2 \times 26) +2$

$=\sf 52+2$

$\sf =54$

Therefore, the length and breadth of the swimming pool is 54 m and 26 m respectively