Question

area of the 4 walls of a hall is 5520 m sq.if the height and length of the room are in the ratio of 3:4 and the height and breadth in the ratio 5:1 then find the area of the floor

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{l},\mathrm{b}\mathrm{and}\mathrm{h}\mathrm{be}\mathrm{the}\mathrm{length},\mathrm{breadth}\mathrm{and}\mathrm{height}\mathrm{of}\mathrm{the}\mathrm{room}. \\ \mathrm{Now}, \\ \frac{\mathrm{h}}{\mathrm{l}}=\frac{3}{4} \\ \Rightarrow \mathrm{l}=\frac{4\mathrm{h}}{3}.....\left(1\right) \\ \mathrm{Now}, \\ \frac{\mathrm{h}}{\mathrm{b}}=\frac{5}{1} \\ \Rightarrow \mathrm{h}=5\mathrm{b}......\left(2\right) \\ \mathrm{Now},\mathrm{from}\left(1\right),\mathrm{we}\mathrm{get} \\ \mathrm{l}=\frac{20\mathrm{b}}{3} \\ \mathrm{Now},\mathrm{area}\mathrm{of}4\mathrm{walls}=5520{\mathrm{m}}^2 \\ \Rightarrow 2\left(\mathrm{l}+\mathrm{b}\right)\mathrm{h}=5520 \\ \Rightarrow \left(\frac{20\mathrm{b}}{3}+\mathrm{b}\right)5\mathrm{b}=2760 \\ \Rightarrow \frac{23\mathrm{b}}{3}\times 5\mathrm{b}=2760 \\ \Rightarrow {\mathrm{b}}^2=\frac{2760\times 3}{23\times 5}=72 \\ \Rightarrow \mathrm{b}=6\sqrt{2}\mathrm{m} \\ \mathrm{Now},\mathrm{l}=\frac{20\mathrm{b}}{3}=\frac{20}{3}\times 6\sqrt{2}=40\sqrt{2}\mathrm{m} \\ \mathrm{area}\mathrm{of}\mathrm{floor}=\mathrm{l}\times \mathrm{b}=40\sqrt{2}\times 6\sqrt{2}=480{\mathrm{m}}^2 \end{gathered}$$