Math CentralQuandaries & Queries


Question from avien, a student:

a rectangle has a line of fixed length L reaching from the vertex to the midpoint of one of the far sides. what is the maximum possible area of such a rectangle? SHOW SOLUTION USING CALCULUS


Suppose the sides of the rectangle are of length x and y.


The area of the rectangle is

area = xy square units.

Look at the diagram. What does Pythagoras theorem tell you about the relationship among x, y and L? Use this to write the area as a function involving only x and L. L is fixed (a constant) so you can use the calculus you know to find the value of x that maximizes the area.


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