EX.2.2 Q2 Linear Equations in One Variable Solutions - NCERT Maths Class 8

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Question

The perimeter of a rectangular swimming pool is \(154 \,\rm{m}\). Its length is \(2 \,\rm{m}\) more than twice its breadth. What are the length and the breadth of the pool?

Text Solution

What is known?

(i) Perimeter of a rectangular swimming pool is \(154\,\rm{m}\).

(ii) Its length is \(2\,\rm{m}\) more than twice its breadth.

What is unknown?

Length and breadth of the pool.

Reasoning:

Form a linear equation by using the formula for the perimeter of a rectangle. Assume either the breadth or the length to be a variable.

Steps:

Let the breadth of swimming pool be \(x \,\rm{m}\).

Therefore, the length of the swimming pool will be \( (2x + 2)\,\rm{m}\)

Perimeter of rectangular swimming pool: \(2(\text{Length + Breadth})\)

Therefore, \(2(x + 2x + 2) = 154\)

\[\begin{align}3x + 2 &= \frac{{154}}{2}\\3x + 2 &= 77\\3x &= 77 - 2\\3x &= 75\\x &= \frac{{75}}{3}\\x &= 25\\{\rm{breadth}} &= 25\,{\rm{m}}\\{\rm{length}} &= 2x + 2\\ &= 2(25) + 2\\ &= 52\,{\rm{m}}\end{align}\]

Length of the pool \(= 52 \,\rm{m}\)

Breadth of the pool \(= 25 \;\rm{m}\)