Evan drew a scale drawing of a campground. The picnic area, which is 100 yards long in real life, is 8 inches long in the drawing. What is the scale factor of the drawing?

Question

Simplify your answer and write it as a ratio, using a colon.

GPT-4o mini · Answer

To find the scale factor of the drawing, we need to compare the lengths in the real life to the lengths in the drawing.

The real-life length of the picnic area is 100 yards, and the length in the drawing is 8 inches. First, we need to convert the real-life length from yards to inches, since the drawing is in inches.

1 yard = 36 inches, so: 100 yards = 100 × 36 inches = 3600 inches.

Now we can set up the scale factor as a ratio of the drawing length to the real-life length:

Scale factor = Drawing Length : Real Life Length Scale factor = 8 inches : 3600 inches.

Next, we simplify the ratio: To simplify, we can divide both sides of the ratio by 8:

8 ÷ 8 : 3600 ÷ 8 1 : 450.

Thus, the scale factor of the drawing is: 1 : 450.