Question

A ladder 50 dm long when set against the wall of a house just reaches a window at a height of 48 dm. How far is the lower end of the ladder from the base of the wall?

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{the}\mathrm{distance}\mathrm{of}\mathrm{the}\mathrm{lower}\mathrm{end}\mathrm{of}\mathrm{the}\mathrm{ladder}\mathrm{from}\mathrm{the}\mathrm{wall}\mathrm{be}\mathrm{X}\mathrm{m}. \\ \mathrm{On}\mathrm{using}\mathrm{the}\mathrm{Pythagoras}\mathrm{theorem},\mathrm{we}\mathrm{get}: \\ {\mathrm{X}}^2+{48}^2={50}^2 \\ \Rightarrow {\mathrm{X}}^2={50}^2-{48}^2=2500-2304=196 \\ \Rightarrow \mathrm{X}=14\mathrm{dm} \\ \mathrm{Hence},\mathrm{the}\mathrm{distance}\mathrm{of}\mathrm{the}\mathrm{lower}\mathrm{end}\mathrm{of}\mathrm{the}\mathrm{ladder}\mathrm{from}\mathrm{the}\mathrm{wall}\mathrm{is}14\mathrm{dm}. \end{gathered}$$