Question

Mark the correct alternative in the following question:

The length of a rectangle is three times its width and its perimeter 56 m. The length is

(a) 7 m (b) 14 m (c) 21 m (d) 28 m

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{the}\mathrm{width}\mathrm{of}\mathrm{the}\mathrm{rectangle}\mathrm{be}x.\mathrm{Then}, \\ \mathrm{the}\mathrm{length}\mathrm{of}\mathrm{the}\mathrm{rectangle}=3x \\ \mathrm{As},\mathrm{perimeter}\mathrm{of}\mathrm{the}\mathrm{rectangle}=56\mathrm{m} \\ \Rightarrow 2\times \left(\mathrm{Length}+\mathrm{Breadth}\right)=56 \\ \Rightarrow 2\times \left(3x+x\right)=56 \\ \Rightarrow 2\times 4x=56 \\ \Rightarrow 8x=56 \\ \Rightarrow x=\frac{56}{8} \\ \therefore x=7 \\ \mathrm{So},\mathrm{the}\mathrm{length}\mathrm{of}\mathrm{the}\mathrm{rectangle}=3x=3\times 7=21\mathrm{m} \end{gathered}$$

Hence, the correct alternative is option (c).