A boy of height 120 cm is walking away from the base of a lamp post at a speed of 87m/ minutes .If the lamp post is 36m above the ground, find the length of his shadow after 3 minutes
Answers
Given :- A boy of height 120 cm is walking away from the base of a lamp post at a speed of 87m/ minutes .If the lamp post is 36m above the ground . find the length of his shadow after 3 minutes ?
Solution :-
From image we have :-
- AB = 36m = Lamp post .
- AD = Distance covered by boy = 87 * 3 = 261m.
- CD = shadow of boy after three minutes, when she at position D = Let x.
- ED = Height of boy = 120 cm. = 1.2m .
In ∆CDE and ∆CAB we have,
→ ∠CDE = ∠CAB (90°)
→ ∠DCE = ∠ACB (Common)
So,
→ ∆CDE ∼ ∆CAB (By AA similarity.)
Than,
→ DE / AB = CD / AC
→ 1.2/ 36 = x/(261 + x)
→ 1/30 = x / (261 + x)
→ 30x = 261 + x
→ 30x - x = 261
→ 29x = 261
→ x = 9 m .(Ans.)
Hence, Length of shadow after 3 minutes is 9m.
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