Q3 of 42 Page 210

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.

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


More from this chapter

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1

In the given figure, ∠ADE = ∠B

i. Show that ΔABC ~ ΔADE


ii. If AD = 3.8cm, AE = 3.6 cm, BE = 2.1cm, BC = 4.2cm. find DE.


 2

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 4

Given that Δ ABC ∼ Δ PQR, CM and RN are respectively the medians of Δ ABC and Δ PQR Prove that

i. Δ AMC ∼ Δ PNR


ii.


iii. ΔCMB ∼ ΔRNQ


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