Question

6. What is the rectangle of maximal area constructed with its base on the diameter of a semicircle of radius

   14 m with its vertices on the semicircle.

Answer 1

Firstly, we will draw diagram

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now, we can use Pythagoras theorem

now, we can solve for l

now, we can find area

now, we can find derivative

now, we can set it to 0

and then we can solve for w

now, we can find length

Dimensions of rectangle:

Length is

Width is