Question

Two vertical poles $AL$ and $BM$ of heights $25m$ and $100m$ respectively stand apart on a horizontal plane. If $A,B$ be the feet of the poles and $AM$ and $BL$ intersect at $P,$ then the height of $P$ from the horizontal plane is equal to

• A. $20m$
• B. $18m$
• C. $16m$
• D. $15m$

Answer 1

Answer: (A)

$\frac{25}{x + y}=\frac{z}{y}\left\{\because \Delta L A B \sim \Delta P N B\right\}$
$\Rightarrow y=\frac{z \left(x + y\right)}{25}\ldots \left(i\right)$
Also, $\frac{100}{x + y}=\frac{z}{x}\left\{\because \Delta M B A \sim \Delta P N A\right\}$
$\Rightarrow x=\frac{z \left(x + y\right)}{100}\ldots \left(i i\right)$
Adding equation $\left(i\right)\&\left(i i\right)$ , we get
$x+y=\left(x + y\right)\left(\frac{z}{25} + \frac{z}{100}\right)\Rightarrow z=20$