Question

chaya has a map that shows the lengths of some hiking trails. the scale is shown in the drawing.
what number can you multiply each distance in
the scale drawing by to find the actual distance?
0.5
what is the actual length of the waterfall trail?
km
length in
scale drawing · 0.5 = actual
length
an error has occurred. please enter a number.

Explanation:

Step1: Determine the multiplier

The scale is \(3\ cm:1.5\ km\). To find the multiplier, we divide the actual distance by the scale - drawing distance. Let \(x\) be the multiplier. If the scale is \(d_{scale}\) (in cm) and \(d_{actual}\) (in km), then \(x=\frac{d_{actual}}{d_{scale}}\). Given \(d_{scale} = 3\ cm\) and \(d_{actual}=1.5\ km\), \(x=\frac{1.5}{3}=0.5\).

Step2: Calculate the actual length of the waterfall trail

The length of the waterfall - trail on the scale drawing is \(d_{scale - waterfall}=6\ cm\). Using the formula \(d_{actual}=d_{scale}\times x\), substitute \(d_{scale}=6\ cm\) and \(x = 0.5\). Then \(d_{actual}=6\times0.5\).

$$6\times0.5=(6\times\frac{1}{2}) = 3$$

Answer:

3