Question

Mark (✓) against the correct answer
Two poles of heights 6 m and 11 m stand vertically on a plane ground. If the distance between their feet is 12 m, what is the distance between their tops?

(a) 13 m
(b) 14 m
(c) 15 m
(d) 12.8 m

Answer 1

$$\begin{gathered} \left(a\right)13\mathrm{m} \\ \mathrm{Suppose}\mathrm{there}\mathrm{are}\mathrm{two}\mathrm{poles}\mathrm{AE}\mathrm{and}\mathrm{BD}. \\ \mathrm{EC}=\mathrm{AB}=12\mathrm{m}(\mathrm{ABCE}\mathrm{is}\mathrm{a}\mathrm{rectangle}) \\ \mathrm{AE}=\mathrm{BC}=6\mathrm{m}(\mathrm{ABCE}\mathrm{is}\mathrm{a}\mathrm{rectangle}) \\ \mathrm{DC}=\mathrm{BD}-\mathrm{AE} \\ =11-6 \\ =5\mathrm{m} \\ \mathrm{In}\mathrm{the}\mathrm{right}\mathrm{angled}\mathrm{triangle}\mathrm{ECD}: \\ {\mathrm{ED}}^2={\mathrm{EC}}^2+{\mathrm{DC}}^2(\mathrm{Pythagoras}\mathrm{theorem}) \\ {\mathrm{ED}}^2=5^2+{12}^2 \\ {\mathrm{ED}}^2=25+144 \\ {\mathrm{ED}}^2=169 \\ \mathrm{ED}=\pm 13 \\ \mathrm{The}\mathrm{length}\mathrm{cannot}\mathrm{be}\mathrm{negative}. \\ \therefore \mathrm{ED}=13\mathrm{m} \end{gathered}$$