Question

The length of a hall is 3 metres more than its breadth. If the area of the hall is 238 square metres, calculate its length and breadth.

Answer 1

$$\begin{gathered} \begin{array}{l}\\ \text{Let the breadth of the rectangular hall be}x\text{metre.}\end{array} \\ \text{Therefore, the length of the rectangular hall will be}(x+3)\text{metre.} \\ \mathrm{According}\mathrm{to}\mathrm{the}\mathrm{question}: \\ x(x+3)=238 \\ \Rightarrow x^2+3x=238 \\ \Rightarrow x^2+3x-238=0 \\ \Rightarrow x^2+(17-14)x-238=0 \\ \Rightarrow x^2+17x-14x-238=0 \\ \Rightarrow x(x+17)-14(x+17)=0 \\ \Rightarrow (x+17)(x-14)=0 \\ \Rightarrow x=-17\text{or}x=14 \\ \text{But the value}x\text{cannot be negative.} \\ \mathrm{Therefore},\mathrm{the}\text{breadth of the hall is 14 metre and the length is 17 metre.} \end{gathered}$$