Question

A girl of height $90cm$ is walking away from the base of a lamp post at a speed of $1.2m/sec$. If the lamp post is $3.6m$ above the ground, find the length of her shadow after 4 seconds.

Answer 1

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 4 sec

Consider $△ABC$ and $△DEC$
$$\begin{array}{cc}& \Rightarrow \angle ABC=\angle DEC={90}^{\circ }\\ & \Rightarrow \angle ACB=\angle DCE\\ & \Rightarrow △ABC\sim \Delta DEC\end{array}$$
$\Rightarrow$ 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.
$\Rightarrow$ we have $\frac{DE}{AB}=\frac{CE}{BC}$
$\Rightarrow \frac{0.9}{3.6}=\frac{CE}{CE+EB}$
$\Rightarrow \frac{1}{4}=\frac{x}{x+4.8}$
$\Rightarrow x+4.8=4x$
$\Rightarrow 4x-x=4.8$
$\Rightarrow 3x=4.8$
$\Rightarrow x=\frac{4.8}{3}$
$\Rightarrow x=1.6m$
$$CE=1.6m$$
Hence, the length of her shadow after $4sec$ is $1.6m$