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The sum of the perimeter of a circle and a square is k, where k is some constant. Prove that the sum of their areas is least when the side of square is double the radius of the circle.
cbse
class12
modelpaper
2011
sec-c
q24
math
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asked
Dec 28, 2012
by
thanvigandhi_1
edited
Dec 29, 2012
by
thanvigandhi_1
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The sum of the perimeter of a circle and square is \(k\), where \(k\) is some constant. Prove that the sum of their areas is least when the side of square is double the radius of the circle.
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Given the sum of the perimeters of a square and a circle show that the sum of their areas is least when the side of the square is equal to the diameter of a circle.
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If the sum of the lengths of the hypotenuse and a side of a right angled triangle is given, show that the area of traingle is maximum when the angle between them is \( \large\frac{\pi}{3} \).
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Show that of all the rectangles of given area, the square has the smallest perimeter.
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