Chapter 11.3, Problem 4P

John has a paper square that he believes is 100 cm wide and 100 cm long, but in reality, the square is actually 1% longer and 1% wider than he believes. In other words, John’s square is actually 101 cm wide and 101 cm long

1. Since John believes the square is 100 cm by 100 cm, he calculates that the area of his square is 10,000 $c{m}^2$ . What percent greater is the actual area of the square than John's calculated area of the square? Is the actual area of John's square 1% greater than John's calculated area, or is it larger by a different percent?

Draw a picture (which need not be to scale) to show why your answer in part (a) is not surprising.

Answer the following questions based on your answers to parts (a) and (b): In general, if you want to know the area of a square to within 1% of its actual area, will it be good enough to know the lengths of the sides of the square to within 1% of their actual lengths? If not, will you need to know the lengths more accurately or less accurately?