Problem:
A triangle has side lengths , , and . A rectangle has width and area equal to the area of the triangle. What is the perimeter of this rectangle?
Answer Choices:
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Solution:
Let the triangle be with , and let be the foot of the altitude from . Then is a right triangle with hypotenuse and one leg . By the Pythagorean Theorem , and the area of is . The rectangle has length and perimeter .
The problems on this page are the property of the MAA's American Mathematics Competitions