question_answer 3)

                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?

Answer:

                Let the breadth of the pool be \[xm\]. \[\because \]     Its length is 2 m more than twice its breadth. \[\therefore \] Length of the tank \[=(2x+2)m\] \[\therefore \] Perimeter of the tank \[=2\times \](Length + Breadth) \[=2\times \,(2x+2+x)\] \[=2\times (3x+2)\] \[=(6x+4)m\] \[\because \]     The perimeter of a rectangular swimming pool is 154 m. \[\therefore \]  \[6x+4=154\] \[\Rightarrow \]               \[6x=154-4\]                      | Transposing 4 to RHS \[\Rightarrow \]               \[6x=150\] \[\Rightarrow \]               \[x=\frac{150}{6}=25\]                   | Dividing both sides by 6 \[\Rightarrow \]               \[2x+2=2\times 25+2\] \[=50+2=52\] Hence, the length and breadth of the pool are 52 m and 25 m respectively. Check: \[52=2\times 25+2\]                        | as desired \[2\times (52+25)=2\times 77=154\].