Final answer:
By setting up a proportion based on the similarity between the shapes of the doghouse and Jane's house, we find that the length of the base of Jane's house is 24 feet.
Step-by-step explanation:
To find the length of the base of Jane's house, we will use the concept of similar figures and set up a proportion based on the given information. Spot's doghouse, which is similar in shape to Jane's house, has a base of 3 feet and a height of 3.5 feet. With Jane's house having a height of 28 feet, we want to determine the length of its base.
The proportion will be based on the idea that corresponding sides of similar figures are proportional. Since the shapes are similar, the ratio of Spot's doghouse's base to its height will be equal to the ratio of Jane's house's base to its height:
Base of doghouse / Height of doghouse = Base of Jane's house / Height of Jane's house
3 feet / 3.5 feet = Base of Jane's house / 28 feet
By cross-multiplying, we get:
3 feet * 28 feet = 3.5 feet * Base of Jane's house
Base of Jane's house = 3 * 28 / 3.5
Base of Jane's house = 24 feet
Therefore, the length of the base of Jane's house is 24 feet.