AboutAbe Mantell Expertise Hello,
I am a college professor of mathematics and regularly teach all levels
from elementary mathematics through differential equations, and would
be happy to assist anyone with such questions!
Experience Over 15 years teaching at the college level.
If two sides of a triangle are of length a and b,
find the length of the third side of the triangle in terms of a and b, that maximizes the
area of the triangle.
Thank you
Answer Since the area of a triangle can be written as:
A=(1/2)(a)(b)sin(C), where C is the angle between the two sides.
So, the maximum area will be when sin(C) is as large as possible.
Thus, C=90 degrees so that sin(C)=1...thus the 3rd side will be
the hypotenuse of the right triangle with legs a and b...
(a^2 + b^2)^(1/2)
