Question:
A rectangle with the largest possible area is inscribed in a semi-circle. Find the ratio of the larger side to the smaller side.
A rectangle with the largest possible area is inscribed in a semi-circle. Find the ratio of the larger side to the smaller side.
Updated On: May 17, 2024
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Solution and Explanation
The correct answer is: 2:1.
There are no critical points in the feasible domain.
Since there are no critical points, we need to consider the boundary points.
Now \((\frac{l}{2})^2=b^2=>I=2b\)
\(\frac{l}{2}=\frac{2}{1}\)
Therefore, the ratio of the larger side to the smaller side of the rectangle with the largest possible area inscribed in a semi-circle is 2:1.
There are no critical points in the feasible domain.
Since there are no critical points, we need to consider the boundary points.
Now \((\frac{l}{2})^2=b^2=>I=2b\)
\(\frac{l}{2}=\frac{2}{1}\)
Therefore, the ratio of the larger side to the smaller side of the rectangle with the largest possible area inscribed in a semi-circle is 2:1.
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