Chapter 1.2, Problem 61E

Challenge yourself

a) Repeat Exercise 59 , but now count rectangles of all types, including squares. b) Repeat Exercise 60, now counting rectangles of all types, including squares. It is important when doing this that you are systematic. Count rectangles of sizes $1\times 1,1\times 2,1\times 3,1\times 4,2\times 1,2\times 2,$ and so on.

59. We will call the rectangle shown here, which has three rows and four columns, a $3\times 4$ rectangle. How many squares of various sizes can you find in this rectangle?

60. Repeat Exercise 59 for a $6\times 4$ rectangle.