Final answer:
The scale of the drawing where a tree is 3 inches tall and its actual height is 18 feet is 1 inch to 6 feet. This is found by converting the actual height to inches and then creating a simplified ratio between the drawing height and the actual height.
Step-by-step explanation:
The question asks to determine the scale of the drawing given that the height of a tree is 3 inches on the scale drawing and its actual height is 18 feet. To find the scale, we will set up a ratio comparing the drawing measurement to the actual measurement, keeping the units consistent.
To convert feet to inches (since the drawing is measured in inches), recall that 1 foot = 12 inches. Therefore, 18 feet is equal to 18 × 12 inches.
Calculation:
18 feet × 12 inches/foot = 216 inches (actual height in inches)
Now we create a ratio: Drawing height / Actual height = 3 inches / 216 inches
This ratio can be simplified by dividing both sides by 3, resulting in a scale factor of 1 inch / 72 inches.
Since 1 inch in the drawing represents 72 inches in actual size, and there are 12 inches in a foot, we can then express the scale as:
Scale: 1 inch = 6 feet (since 72 inches is equivalent to 6 feet).