Final answer:
The scale factor of 2 inches : 3 feet is used to determine the length of the model boat. A proportion is set up and solved to find that the model boat is 20 inches long, which is option c.
Step-by-step explanation:
Understanding Scale Models. When dealing with scale models, it's important to use the given scale factor to determine the corresponding dimensions of the model or the real object. In this case, the scale given is 2 inches for every 3 feet of the actual boat. To find out the length of the model boat when the real boat is 30 feet long, set up a proportion based on the scale:
- Scale ratio: 2 inches (model) / 3 feet (real)
- Actual boat length: 30 feet
Convert feet to inches since the model is measured in inches (1 foot = 12 inches) and set up the proportion:
2 inches (model) / 36 inches (real) = x inches (model) / 360 inches (real)
Cross multiply to solve for x:
2 * 360 = 36 * x
720 = 36x
x = 720 / 36
x = 20 inches
Therefore, the model boat is 20 inches long. This corresponds to option c.