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A window is in the form of a rectangle, surm ounted by a semicircle. If the
perimeter is 30 inches, find the dimensions so that the greatest possible amount of light may be admitted.
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Given the sum of the perimeters of a square and circle, show that the sum of their
areas is least when the side of the square is equal to the diameter of the circle.
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Show that of all the rectangle inscribed in a given circle, the square has the
maximum area.
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A right angled triangle ABC with constant area S is given. Prove that the
hypotenuse of the triangle is least when the triangle is isosceles.
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A wire of given lenght is cut into the portions which are divided into shapes of
a circle and a square respectively. Show that the sum of the areas of the circle
and the square will be least when one side of the square is equal to the diameter
of the circle.
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A wire of 28 inch is to be cut into two pieces. One of the two pieces to be made
into a square and the other into a circle. What should be the length of the two
pieces so that the combined area of them is minimum?
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