Final answer:
To find the height of the Statue of Liberty in a new drawing with a scale of 1 inch to 20 feet, multiply the height from the old drawing (3 inches) by the old scale (100 feet per inch) to find the actual height (300 feet). Then divide by the new scale (20 feet per inch) to find the new height in the drawing (15 inches).
Step-by-step explanation:
The problem involves scale drawings and proportions. We need to calculate how tall the Statue of Liberty will be in a new drawing made using a scale of 1 inch to 20 feet, based on another drawing that used a scale of 1 inch to 100 feet. Since the Statue of Liberty is 3 inches tall in Nikhil's drawing, we find out how many feet it represents and then convert that measurement into inches using the new scale.
First, we can find the actual height represented by Nikhil's drawing using his scale factor. So, 3 inches in Nikhil's drawing represents 3 inches × 100 feet/inch = 300 feet. Now using the new scale factor of 1 inch to 20 feet, we set up the proportion: If 1 inch corresponds to 20 feet, then how many inches would represent 300 feet? We can calculate this by dividing 300 feet by 20 feet/inch to get the result in inches.
300 feet ÷ 20 feet/inch = 15 inches. This means that in the new drawing, the Statue of Liberty will be 15 inches tall.