Question

The height of the two buildings is 34 m and 29 m respectively. The distance between their top is 13 m, then the distance between the two buildings is.

• A. $16m$
• B. $13m$
• C. $12m$
• D. $14m$

Answer 1

The correct option is C $12m$

The vertical buildings AB and CD are 34 m and 29 m respectively.

Draw DE $\perp$ AB.

Then $AE=AB–EBbutEB=DC$

Therefore $AE=34-29=5m$

Now, AED is a right angled triangle and right angled at E.

Therefore,

$A{D}^2=A{E}^2+E{D}^2$

$\Rightarrow {13}^2=5^2+E{D}^2$

$\Rightarrow 169=25+E{D}^2$

$\Rightarrow E{D}^2=169-25$

$\Rightarrow ED=\sqrt{144}$

$\Rightarrow ED=12$

Therefore, the distance between the two buildings = $12m$