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
waterfall
parking
picnic
area
ranger
tower
3 cm:1.5 km

Explanation:

Step1: Find the scale factor

Given the scale \(3\ cm:1.5\ km\). To find the multiplier, divide the actual distance by the map distance. Let the multiplier be \(k\). We have \(k=\frac{1.5}{3}\).

$$k = 0.5$$

Step2: Calculate the actual length of the waterfall trail

The length of the waterfall - trail on the map is \(6\ cm\). Using the multiplier \(k = 0.5\) (where the unit of \(k\) is \(\frac{km}{cm}\)), the actual length \(L\) is \(L=\text{map distance}\times k\).

$$L=6\times0.5$$

$$L = 3$$

Answer:

The number to multiply is \(0.5\). The actual length of the waterfall trail is \(3\ km\).