21 - 24 Solved problems in maxima and minima

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Problem 21
Find the rectangle of maximum perimeter inscribed in a given circle.

Solution:

 

Problem 22
If the hypotenuse of the right triangle is given, show that the area is maximum when the triangle is isosceles.

Solution:

 

Problem 23
Find the most economical proportions for a covered box of fixed volume whose base is a rectangle with one side three times as long as the other.

Solution:

 

Problem 24
Solve Problem 23 if the box has an open top.

Solution:

 

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