largest area

Problem
Find the area of the largest right triangle whose hypotenuse is fixed at c.
 

         

Problem
The line y = 2x + 8 intersects the parabola y = x² at points A and B. Point C is on the parabolic arc AOB where O is the origin. Locate C to maximize the area of the triangle ABC.
 

Situation
A right circular cone has a base diameter of 24 cm. The maximum area of parabolic segment that can be cut from this cone is 207.8 cm².
 

Part 1: Determine the base width of the parabola.
A. 22.32 cm
B. 18.54 cm
C. 15.63 cm
D. 20.78 cm
 

Part 2: Determine the altitude of the parabola.
A. 14 cm
B. 18 cm
C. 15 cm
D. 16 cm
 

Part 2: Determine the altitude of the cone.
A. 20 cm
B. 14 cm
C. 16 cm
D. 18 cm