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Class 12 Tuition > Learn Exercise 6.5 > Show that of all the rectangles inscribed in a...
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Show that of all the rectangles inscribed in a given fixed circle, the square has the maximum area.

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Let a rectangle of length l and breadth b be inscribed in the given circle of radius a. Then, the diagonal passes through the centre and is of length 2a cm. Now, by applying the Pythagoras theorem, we have: ∴Area of the rectangle, By the second derivative test, when, then the area of the...
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Let a rectangle of length l and breadth b be inscribed in the given circle of radius a. Then, the diagonal passes through the centre and is of length 2a cm. Now, by applying the Pythagoras theorem, we have: ∴Area of the rectangle, By the second derivative test, when, then the area of the rectangle is the maximum. Since, the rectangle is a square. Hence, it has been proved that of all the rectangles inscribed in the given fixed circle, the square has the maximum area. read less
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Related Questions

For all real values of x, the minimum value of  is

(A) 0 (B) 1

(C) 3 (D)

Let ∴By second derivative test, f is the minimum at x = 1 and the minimum value is given by . The correct answer is D.
Chiranjeevi
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