Problem:
Four congruent rectangles are placed as shown. The area of the outer square is 4 times that of the inner square. What is the ratio of the length of the longer side of each rectangle to the length of its shorter side?
.jpg)
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Let the lengths of the shorter and longer side of each rectangle be and , respectively. The outer and inner squares have side lengths and , respectively, and the ratio of their side lengths is . Therefore , from which .
The problems on this page are the property of the MAA's American Mathematics Competitions