Difference between revisions of "Course:MATH102/Question Challenge/1998 December Q3"
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Revision as of 15:31, 7 December 2017
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Please rate how easy you found this problem:
Current user rating: 37/100 (4 votes) Hard Easy |
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Question
Find the area of the largest rectangle that can be inscribed in the semi-circle of radius .
Hints
Hint 1 |
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Use the coordinates to label the point on the circle at the corner of the rectangle. What is the relationship between , , and ? This relationship will be a constraint in this optimization problem. |
Hint 2 |
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What is the width and height of the rectangle in terms of and ? |
Hint 3 |
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Write down the area of the rectangle in terms of and , then use the constraint to eliminate either or . |
Solutions
Solution |
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Area = a^2 |