Two poles of heights 10 m and 15 m, stand on a plane ground. If the distance between their feet is 12 m, the distance between their tops is

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Two poles of heights 10 m and 15 m, stand on a plane ground. If the distance between their feet is 12 m, the distance between their tops is

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12 m

13 m

12.5 m

13.5 m

answer is B.

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Detailed Solution

Given that two poles of heights 10 m and 15 m, stand on a plane ground and the distance between their feet is 12 m.
Question Image

Let us draw a perpendicular from

B

CD

which meets

CD

P

.
It is clear that

BP = 12 m

because it is given that distance between feet of the two poles is

12 m

.
After drawing the perpendicular we get a rectangle

BACP

such that

AB = PC

and

BP = AC

.
Because of this construction we also obtained a right angled triangle

BPD

.
Now by Pythagoras theorem,

B D^{2} = B P^{2} + D P^{2}

B D^{2} = 12^{2} + 5^{2} [∵ DP = DC - PC = 15 - 10 = 5 m]

\Rightarrow B D^{2} = 144 + 25

\Rightarrow B D^{2} = 169

\Rightarrow BD = 13

m .
Therefore, distance between the top of the two poles is

13 m

.
Hence

2

is the correct option.

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