Question

what number can you multiply each distance in the scale drawing by to find the actual distance?
what is the actual length of the waterfall trail?

Explanation:

Step1: Find the scale factor

The scale is \(3\) cm : \(1.5\) km. First, convert km to cm. Since \(1\) km \( = 100000\) cm, \(1.5\) km \(=1.5\times100000 = 150000\) cm.
The scale factor is \(\frac{150000}{3}=50000\). So, we multiply each distance in the scale drawing by \(50000\) cm per cm (or \(0.5\) km per cm, since \(50000\) cm \(=0.5\) km) to find the actual distance.

Step2: Calculate the actual length of the waterfall trail

The length of the waterfall trail in the scale drawing is \(6\) cm.
Using the scale factor of \(0.5\) km per cm, the actual length \(L = 6\times0.5\) km.

Answer:

The number to multiply each distance in the scale drawing is \(0.5\) km per cm. The actual length of the waterfall trail is \(3\) km.