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Q.

A vertical pole of length 6 m casts a shadow 4 m long on the ground and at the same time a tower casts a shadow 28 m long. What is the height of the tower?

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a

25m

b

44m

c

35m

d

42m  

answer is D.

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Detailed Solution

Given that, a vertical pole of length 6 m casts a shadow 4 m long on the ground and at the same time a tower casts a shadow 28 m long.
Let CD be a pole of length 6 meter,
DF = 4 m be the length of its shadow.
Let another tower AB cast shadow BE of length 28 m.
Question ImageThe sun will make equal angles with both the towers at same time.
⇒∠DCF=∠BAE   ……[1]
The poles are upright, so angle with ground is right angle.
⇒∠CDF=∠ABE   ……[2]
From [1] and [2], By AA similarity Criteria,
ΔCDF~ΔABE   We know that if two triangles are similar then their corresponding sides are in proportion and the corresponding angles are equal.
⇒ CD AB = DF BE   Putting values on the equation, we get
⇒ 6 AB = 4 28 ⇒AB= 28 4 ×6 ⇒AB=42m  
Hence, the height of the tower is 42m.
Therefore, the correct option is 4.
 
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