Problem:
The area of each of the four congruent L-shaped regions of this -inch by -inch square is of the total area. How many inches long is the side of the center square?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
The four -shaped regions account for of the total area. That leaves of the total area for the center square, which yields square inches. Thus the length of the side of the center square is inches.
As in the first solution, the center square is of the total area. Dividing the large square into four equal parts as shown yields a square that is by inches.
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions