The shadow of a 5 m long stick is 2 m long. At the same time the length of the shadow of a 12.5 m high tree is:

1. 3 m

2. 3.5 m

3. 4.5 m

4. 5 m

Given,

Suppose DE is a 5 m long stick and BC is a 12.5 m high tree.

Suppose EA and CA are the shadows of DE and BC respectively.

Now, In ΔABC and ΔADE,

∠ACB = ∠AED = 90°

∠A = ∠A [Common]

∴ ΔABC ∼ ΔADE by AA similarity.Then ratios of corresponding sides are equal:

$\Rightarrow \dfrac{CA}{AE} = \dfrac{BC}{DE} \\[1em] \Rightarrow \dfrac{CA}{2} = \dfrac{12.5}{5} \\[1em] \Rightarrow CA = \dfrac{12.5 \times 2}{5} \\[1em] \Rightarrow CA = \dfrac{25}{5} \\[1em] \Rightarrow CA = 5 \text{ cm.}$

Hence, option 4 is the correct option.