Question

As shown in the given figure, two poles of height 8 m and 4 m are perpendicular to the ground. If the length of shadow of smaller pole due to sunlight is 6 m then how long will be the shadow of the bigger pole at the same time ?

Answer 1

Given:
PR = 4
RL = 6
AC = 8
In △PLR and △ABC
∠PRL = ∠ACB (Vertically opposite angles)
∠LPR = ∠BAC (Angles made by sunlight on top are congruent)
By AA test of similarity
△PLR ∼ △ABC
$$\begin{gathered} \therefore \frac{\mathrm{PR}}{\mathrm{AC}}=\frac{{\displaystyle \mathrm{LR}}}{{\displaystyle \mathrm{BC}}}\left(\mathrm{Corresponding}\mathrm{sides}\mathrm{are}\mathrm{proportional}\right) \\ \Rightarrow \frac{4}{8}=\frac{6}{x} \\ \Rightarrow x=12 \end{gathered}$$
Hence, the length of shadow of bigger pole due to sunlight is 12 m.