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
Solution:
(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:
$B D^{2}=B E^{2}+E D^{2}$
$=12^{2}+5^{2} \quad(\because E D=C D-C E=11-6)$
$=144+25=169$
$B D=13 \mathrm{~m}$