Question

Two poles of height 6 m and 11 m stand vertically upright on a plane ground. If the distance between their feet is 12 m, then the distance between their tops is

(a) 12 m
(b) 13 m
(c) 14 m
(d) 15 m

Answer 1

(b) 13 m


Let the poles be AB and CD.
It is given that:
AB = 6 m and CD = 11 m
Let AC be 12 m.
Draw a perpendicular from B on CD, meeting CD at E.
Then,
BE = 12 m
We have to find BD.
Applying Pythagoras theorem in right-angled triangle BED, we have: ​
$$\begin{gathered} B{D}^2=B{E}^2+E{D}^2 \\ ={12}^2+5^2(\because ED=CD\hspace{0.17em}-CE=11-6) \\ =144+25=169 \\ BD\hspace{0.17em}=13\mathrm{m} \end{gathered}$$