Question

Two poles of heights 10 m and 15 m, stand on a plane ground. If the distance between their feet is 12 m, the distance between their tops is

• A. 12 m
• B. 13 m
• C. 12.5 m
• D. 13.5 m

Answer 1

The correct option is B 13 m

Let us draw a perpendicular from $B$ on $CD$ which meets $CD$ at $P$.

It is clear that $BP=12m$ because it is given that distance between feet of the two poles is $12m$.

After drawing the perpendicular we get a rectangle $BACP$ such that $AB=PC$ and $BP=AC$.

Because of this construction we also obtained a right angled triangle $BPD$.

Now we will use Pythagoras theorem,

$B{D}^2=B{P}^2+D{P}^2$

Let us substitute the values of $BP$ and $PD$ we get,

$B{D}^2={12}^2+5^2[\because DP=DC-PC=15-10=5m]$

$\Rightarrow B{D}^2=144+25$

$\Rightarrow B{D}^2=169$

$\Rightarrow BD=13$

Therefore, distance between the top of the two poles is $13m$.

So, $\text{B}$ is correct option.