Problem:
The ratio of the length to the width of a rectangle is . If the rectangle has diagonal of length , then the area may be expressed as for some constant . What is ?
Answer Choices:
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Solution:
Let the sides of the rectangle have lengths and . By the Pythagorean Theorem, the diagonal has length . Because , the side lengths are and . Therefore the area is , so .
The problems on this page are the property of the MAA's American Mathematics Competitions