Question

The perimeter of a rectangle is 82 m and its area is 400 m². The breadth of the rectangle is
(a) 25 m
(b) 20 m
(c) 16 m
(d) 9 m

Answer 1

(c) 16 m

$$\begin{gathered} \text{Let the length and breadth of the rectangle be}l\text{and}b. \\ \text{Perimeter of the rectangle = 82 m} \\ \Rightarrow 2\times (l+b)=82 \\ \Rightarrow l+b=41 \\ \Rightarrow l=(41-b)...\left(\text{i}\right) \\ \mathrm{Area}\mathrm{of}\mathrm{the}\mathrm{rectangle}=400{\text{m}}^2 \\ \Rightarrow l\times b=400{\text{m}}^2 \\ \Rightarrow (41-b)b=400\left(\text{using}\left(\text{i}\right)\right) \\ \Rightarrow 41b-b^2=400 \\ \Rightarrow b^2-41b+400=0 \\ \Rightarrow b^2-25b-16b+400=0 \\ \Rightarrow b(b-25)-16(b-25)=0 \\ \Rightarrow (b-25)(b-16)=0 \\ \Rightarrow b=25\text{or}b=16 \\ \mathrm{If}b=25,\mathrm{we}\mathrm{have}: \\ l=41-25=16 \\ \mathrm{Since},l\mathrm{cannot}\mathrm{be}\mathrm{less}\mathrm{than}\mathrm{b}, \\ \therefore b=16\text{m} \end{gathered}$$