Q) As shown in the given figure, a girl of height 90 cm is walking away from the base of a lamp post at a speed of 1.2 m/s. If the lamp is 3.6 m above the ground, find the length of her shadow after 4 seconds.

(Q 35 B – 30/2/2 – CBSE 2026 Question Paper)

Ans: 

Step 1: In Δ ABE and Δ CDE,

∠ ABE = ∠ CDE   (Right angles – given)

∠ E  = ∠ E  (common angle)

∴   Δ ABE ~ Δ CDE   (by AA similarity identity)

Step 2: Let’s calculate length of BD

It is equal to the distance travelled in 4 secs

∵ Speed of girl = 1.2 m/s

and time = 4 secs

∴ Distance travelled in 4 secs = Speed x Time

= 1.2 x 4 = 4.8 m

Step 3: Next, from above similar triangles,

we have

∵ BE = BD + DE

∴

∴

∴ 4 DE = 4.8 + DE

∴ 3 DE = 4.8

∴ DE = = 1.6 m

Therefore, the length of her shadow after 4 seconds is 1.6 m.

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