Barge Math Competition - Spring Semester

Week 6’s Problem: Boxed In

The diagram below shows ten rectangles arranged in something of a staircase pattern. The four values A, B, C, and D are vertical distances, whereas a, b, c, and d are horizontal distances. These eight distances are allowed to take on any real value, with the restriction that each of the ten rectangles must have area that is an integer, and the ten rectangle areas must all be distinct.

As an example, if A = 1/5, then the value of c could be 10, but cannot be 7. If A = 1/5 and c = 10, then only the rectangle with side lengths A and c can have area 2.

For this week’s problem, find values for the eight variables that satisfy the restriction and that make the total area of the ten rectangles as small as you can. Is your answer the best possible?

How to submit your answer:

Bring your solution to the Math Department office in 230 Pardee, or send it by email to Ethan Berkove at berkovee@lafayette.edu. Problem #6 is due by the end of the day on Friday, March 31.