Question

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

(a) 3 m

(b) 3.5 m

(c) 4.5 m

(d) 5 m

Answer 1

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

Suppose DA and BA are the shadows of DE and BC respectively.

Now, In $△$ ABC and $△$ ADE

$\angle ABC=\angle ADE={90}^o\angle A=\angle A$

By AA- similarity criterion

$△ABC\sim △ADE$

If two triangles are similar, then the ratio of their corresponding sides are equal.

$\therefore \frac{AB}{AD}=\frac{BC}{DE}\Rightarrow \frac{AB}{2}=\frac{12.5}{5}\Rightarrow 5AB=25\Rightarrow AB=5m$

Hence, the correct answer is the option (d).