Question

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 picnic area trail? km 3 cm : 1.5 km (diagram with 6 cm, 3 cm, 9 cm, waterfall, parking, ranger tower, picnic area)

Explanation:

First Sub - Question (What number to multiply for actual distance)

Step1: Analyze the scale

The scale is given as \(3\space\text{cm}:1.5\space\text{km}\). To find the multiplier, we calculate the ratio of actual distance to map distance.
The multiplier \(m=\frac{1.5\space\text{km}}{3\space\text{cm}}\)

Step2: Simplify the ratio

\(\frac{1.5}{3} = 0.5\). So we multiply each distance in the scale drawing (in cm) by \(0.5\) to get the actual distance in km.

Step1: Use the multiplier

We know the multiplier from the first part is \(0.5\space\text{km/cm}\). The map length \(l = 6\space\text{cm}\).
The actual length \(L=l\times0.5\)

Step2: Calculate the actual length

\(L = 6\times0.5= 3\space\text{km}\)

Answer:

\(0.5\)

Second Sub - Question (Actual length of picnic area trail)

Assume the length of the picnic area trail on the map is \(6\space\text{cm}\) (from the diagram: the segment labeled for the picnic area trail is \(6\space\text{cm}\)).