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Question
Two trees 7 m and 4 m high stand upright on a ground. If their bases (roots) are 4 m apart, then the distance between their tops is ______.
Options
3 m
5 m
4 m
11 m
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Solution
Two trees 7 m and 4 m high stand upright on a ground. If their bases (roots) are 4 m apart, then the distance between their tops is 5 m.
Explanation:
Let BE be the smaller tree and AD be the bigger tree.
Now, we have to find AB (i.e. the distance between their tops).
By observing,
ED = BC = 4 m and BE = CD = 4 m
In ΔABC, BC = 4 m
And AC = AD – CD = (7 – 4) m = 3 m
In right angled ΔABC,
AB2 = AC2 + BC2 ...[By Pythagoras theorem]
= 42 + 32
= 16 + 9
⇒ AB2 = 25
⇒ AB = `sqrt(25)`
⇒ AB = 5 m
Therefore, the distance between their tops is 5 m.
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