Problem:
Four congruent rectangles are placed as shown. The area of the outer square is 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?
Answer Choices:
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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