Question

The heights of the two buildings are $34m$ and $29m$ respectively. If the distance between the two buildings is 12m, find the distance between the top of the buildings.

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

Answer 1

The correct option is B $13m$

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

Draw DE $\perp$ AB.

Then $AE=AB–EB$ and $EB=DC$

Therefore $AE=34m-29m=5m$

And, $BC=ED=12m$

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

Therefore,

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

$\Rightarrow A{D}^2=5^2+{12}^2$

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

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

$\Rightarrow AD=\sqrt{169}$

$\Rightarrow AD=13$

Therefore the distance between the top of the buildings is $13m$