Question

the scale drawing shows the dimensions of a motel. the scale is shown in the drawing. find the actual length of the east side. what number can you multiply each length in the scale drawing by to find the actual length? motel fire safety map east 2 in. scale = 6 in. : 30 yd

Explanation:

Step1: Find the scale - factor

The scale is $6$ in. : $30$ yd. First, convert the scale to a unit - less ratio. Since $1$ yd=$36$ in, $30$ yd = $30\times36 = 1080$ in. The scale ratio is $\frac{6}{1080}=\frac{1}{180}$. To go from the scale - drawing length to the actual length, we multiply by the reciprocal of the scale ratio. The number to multiply by is $\frac{1080}{6}=180$.

Step2: Calculate the actual length of the east side

The length of the east side in the scale drawing is $2$ in. The actual length $L$ is found by multiplying the scale - drawing length by the conversion factor. $L = 2\times180=360$ in. Convert 360 in to yards. Since $1$ yd = 36 in, $L=\frac{360}{36}=10$ yd.

Answer:

The number to multiply each length in the scale drawing by to find the actual length is 180. The actual length of the east side is 10 yd.