12 Nov 2021
Problem 21
Page 306
Section 4.6: Optimization Problems
Chapter 4: Applications of Differentiation
Textbook ExpertVerified Tutor
12 Nov 2021
Given information
The isosceles triangle of largest area that can be inscribed in a circle of radius .
Step-by-step explanation
Step 1.
As per the given question,
Draw the diagram the isosceles triangle that can be inscribed in a circle of radius .
The area of the triangle is given by . We can write in terms of and .
Now, the area can be written as
Geometrically, is defined only when is in . At the end point the triangle degenerates into a line.
Differentiating we get
Setting to zero gives