Question

Two vertical poles $20m$ and $80m$ high stand a part on a horizontal plane. The height of the point of intersection of the lines joining the top of each pole to the foot of the other is

• A. $13m$
• B. $14m$
• C. $15m$
• D. $16m$

Answer 1

The correct option is D $16m$

$\frac{b}{h}=\frac{a+b}{20}$

$\frac{a}{h}=\frac{a+b}{80}$

$\frac{80}{h}=1+\frac{b}{a}$

$\frac{80-h}{h}=\frac{b}{a}$

$\frac{20}{h}=\frac{a}{b}+1$

$\frac{20}{h}=\frac{h}{(80-h)}+1$

$\frac{20}{h}=\frac{80-h+h}{80-h}$

$100h=1600$

$h=16m$