Q. 34.2( 32 Votes )

# A girl of height 90 cm is walking away from the base of a lamp post at a speed of 1.2m/sec. If the lamp post is 3.6 m above the ground, find the length of her shadow after 4 seconds.

Answer :

Given, a girl with height 90cm and speed 1.2m/sec

And the lamp post is 3.6m above

Need to find the length of her shadow after 4sec

Consider Δ ABC and Δ DEC

⇒ ∠ ABC = ∠ DEC = 90°

⇒ ∠ ACB = ∠ DCE

⇒ Δ ABC ∼ Δ DEC

⇒ By converse proportionality theorem if a line divides any two sides of a triangle in the same ratio then the line must be parallel to the third side.

⇒ we have

⇒

⇒

⇒ x + 4.8 = 4x

⇒ 4x – x = 4.8

⇒ 3x = 4.8

⇒ X =

⇒ X = 1.6m

CE = 1.6m

Hence, the length of her shadow after 4 sec is 1.6m

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