Question

A building casts a shadow 25 m long. At the same time, the shadow cast by a 44-cm tall pole is 59 cm long. Find the height of the building.

 A. 17.1 m B. 32.0 m C. 33.5 m D. 18.6 m

Answer 1

For this, we are going to be using proportions to solve. But firstly, we have to convert cm to m. For this, I'll be using dimensional analysis:

$\frac{44\ cm}{1}*\frac{0.01\ m}{1\ cm}=\frac{0.44}{1}=0.44\ m$

$\frac{59\ cm}{1}*\frac{0.01\ m}{1\ cm}=\frac{0.59}{1}=0.59\ m$

Now that we have everything in meters, we can put it into proportions. In this case, our proportion is $\frac{x}{25} =\frac{0.44}{0.59}$

Firstly, cross-multiply: $0.59x=11$

Next, divide both sides by 0.59, and your answer will be x = 18.6 m, or D.