Q3 of 62 Page 186

A girl of height 120 cm is walking away from the base of a lamp-post at a speed of 0.6 m/sec. If the lamp is 3.6 m above the ground level, then find the length of her shadow after 4 seconds.


Here,


In the figure above,


FE is the height of the girl.


DC is the height of the lamp.


CE is the distance traveled by the girl in 4 seconds.


GE is the shadow of the girl after 4 seconds.


We need to find GE.


CE = 4 × 0.6 m


CE = 240 cm


In ΔGFE and ΔGDC


∠EFG = ∠CDG by corresponding angles (DC∥FE)


∠GFE = ∠GDC by corresponding angles (DC∥FE)


∴ ΔGFE ∼ ΔGDC


(∵ ΔGFE ∼ ΔGDC)




⇒ 3×GE = 240 + GE


⇒ 2×GE = 240


⇒ GE = 120 cm


⇒ GE = 1.2 m


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