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Question

A tower of height 24 m casts a shadow of 50 m and at the same time and on the same side a girl of height 1.8 m casts a shadow. The girl's shadow is of length .

A
3 m
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B
3.5 m
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C
3.75 m
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Solution

The correct option is C 3.75 m

Let AB be the height of tower, BC be the length of the shadow of the tower, ED be the height of the girl and EC = x be the length of her shadow.

In ABC and DEC,
ABC=DEC=90
BCA=ECD
(common in both triangles)

Therefore, ABCDEC
(by AA similarity criterion)

DEAB=ECBC (corresponding sides of similar triangles are in same ratio)
EC=DE×BCAB

EC=1.8×5024

EC=3.75 m

Therefore, length of the her shadow is 3.75 m.


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