Question

what is the actual length of the waterfall trail? km (map shows: waterfall to parking is 6 cm, parking to picnic area is 9 cm, parking to ranger tower is 3 cm; scale 3 cm : 1.5 km)

Explanation:

Step1: Determine the scale

The scale is given as \(3\,\text{cm}:1.5\,\text{km}\). First, find the scale factor per centimeter. Divide the actual distance by the map distance: \(\frac{1.5\,\text{km}}{3\,\text{cm}} = 0.5\,\text{km/cm}\). This means each centimeter on the map represents \(0.5\) kilometers in actual distance.

Step2: Find the map length of the waterfall trail

From the map, the waterfall trail (from Waterfall to Parking) is \(6\,\text{cm}\) long.

Step3: Calculate the actual length

Multiply the map length by the scale factor. So, actual length \(= 6\,\text{cm} \times 0.5\,\text{km/cm} = 3\,\text{km}\).

Answer:

\(3\)