A billboard is 4.0 meters by 2.5 meters. A scale diagram of the billboard must fit in a space that is 15 centimeters by 12 centimeters. Write a reasonable scale for the scale diagram.

15cm:4m is a scale of .0375

12cm:2.5m is a scale of .0480

So, use the smaller scale if it must all fit.

To determine a reasonable scale for the scale diagram, we need to find the ratio of the dimensions of the actual billboard to the dimensions of the space available for the diagram.

First, let's convert the dimensions of the billboard from meters to centimeters:
- Length: 4.0 meters = 400 centimeters
- Width: 2.5 meters = 250 centimeters

Now, we can calculate the ratio:
- Length ratio: 400 cm / 15 cm = 26.67
- Width ratio: 250 cm / 12 cm = 20.83

Since we need to write a reasonable scale for the diagram, we can round the ratios to whole numbers for simplicity.

A reasonable scale for the scale diagram could be:
- Length: 27 cm represents 400 cm
- Width: 21 cm represents 250 cm

To find a reasonable scale for the scale diagram, you need to calculate the ratio between the dimensions of the actual billboard and the dimensions of the diagram.

First, convert the dimensions of the billboard from meters to centimeters, as the dimensions of the diagram are given in centimeters:
Length of billboard = 4.0 meters = 400 centimeters
Width of billboard = 2.5 meters = 250 centimeters

Next, compare the dimensions of the billboard to the dimensions of the diagram:
Length ratio = Length of billboard / Length of diagram = 400 cm / 15 cm
Width ratio = Width of billboard / Width of diagram = 250 cm / 12 cm

Now, simplify the ratios:
Length ratio = 400 cm / 15 cm = 26.67
Width ratio = 250 cm / 12 cm = 20.83

Finally, choose a reasonable scale by rounding the ratios to whole numbers:
Length ratio = 27
Width ratio = 21

Therefore, a reasonable scale for the scale diagram would be 1:27 for the length and 1:21 for the width.