I need help Peter is replacing five broken sections of the picket fence around his house. The length of each section is between 7 and 9 feet, and the height of each section is between 3 and 5 feet. Peter estimates the area of the five sections that need to be replaced to be 200 square feet. Is this a reasonable estimate?

In this question, we want to evaluate how reasonable is an estimate made by Peter.
To do this, we need to have a range , with the boundaries of the range being the lowest expected area and the highest expected areas respectively.
The lowest expected area would take into recognition the lest length and height which is just 3 by 4 . The area of a section here is thus 3 * 4 = 12 sq.feet
Since there are 5 sections, the total area here is thus 12 * 5 = 60 sq.feet. This is the minimum total area of the sections
For the maximum, we compute the area of the sections using the highest length and height. This is 5 by 6. The area here would be 5 * 6 = 30 sq.feet . Since there are 5 sections, the total area here would be 30 * 5 = 150 sq.feet
Hence, we have the area falling between 60 sq.feet and 150 sq.feet
Since the estimates fall between the boundaries and in fact is closer to the maximum, it is a good estimate