Question

At a particular time of a day, a $7m$-high flagstaff casts a shadow which is $8.2m$ long. What is the height of the building which casts a shadow $20.5m$ in length at the same moment?

Answer 1

Height of the flagstaff that casts a shadow of length $8.2m=7m$

Let, Height of the building that casts a shadow of length $20.5m$ be $x$.

Since, When height of the flagstaff increase then its corresponding shadow also increase.

So, this situation in direct proportion.

i.e., Ratio of the quantities is constant.

$\Rightarrow \frac{8.2m}{7m}=\frac{20.5m}{x}$

$\Rightarrow x=20.5m\times \frac{7m}{8.2m}$

$\Rightarrow x=\frac{205\times 7m}{82}$

$\Rightarrow x=\frac{1435m}{82}$

$\Rightarrow x=17.5m$

Therefore, The height of the required building is $17.5m$.