Engineering Board Exam Reviewer · Optimization (Maxima and Minima) · medium
Find the maximum area of a rectangle that can be inscribed in a semicircle of radius 5, with one side on the diameter.
- 25
- 12.5
- 50
- 20
Answer
A. 25
Solution
Let the rectangle have half-width x and height y, with x2+y2=25. Area =2xy, so ( Area)2=4x2(25-x2). Maximizing gives x2=y2=12.5, so Area =2(12.5)=25.
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