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Find the dimensions of the rectangle of largest area that can be inscribed in a circle of radius r. List the dimensions in non- decreasing order (the answer may depend on r).

Find the dimensions of the rectangle of largest area that can be inscribed in a circle of radius r. List the dimensions in non- decreasing order (the answer may depend on r).

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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**Problem Statement:** Find the dimensions of the rectangle of largest area that can be inscribed in a circle of radius \( r \). List the dimensions in non-decreasing order (the answer may depend on \( r \)). **Inputs:** - Two input fields are provided for entering the dimensions. **Instructions:** - Solve for the dimensions so that the area is maximized. - Ensure the dimensions are in non-decreasing order before submitting. Mathematically, this involves using optimization techniques to determine the largest possible area. Typically, the diagonal of the rectangle equals the diameter of the circle (i.e., \( 2r \)), and the optimal rectangle is a square for this arrangement, each side having length \( \sqrt{2}r \). Thus, the solutions entered should confirm or align with these geometrical properties.
Transcribed Image Text:**Problem Statement:** Find the dimensions of the rectangle of largest area that can be inscribed in a circle of radius \( r \). List the dimensions in non-decreasing order (the answer may depend on \( r \)). **Inputs:** - Two input fields are provided for entering the dimensions. **Instructions:** - Solve for the dimensions so that the area is maximized. - Ensure the dimensions are in non-decreasing order before submitting. Mathematically, this involves using optimization techniques to determine the largest possible area. Typically, the diagonal of the rectangle equals the diameter of the circle (i.e., \( 2r \)), and the optimal rectangle is a square for this arrangement, each side having length \( \sqrt{2}r \). Thus, the solutions entered should confirm or align with these geometrical properties.
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