Question

Find the lengths of the base and height of a triangle which will maximize the area of a
triangle under the constraint of those lengths summing to 5.

Answer 1

A=1/2bh
b+h=5 so..
h=5-b plug this into the original equation
A=1/2b(5-b)=5/2b-1/2b^2
take the derivative
A'=5/2-b
find critical numbers/what makes
5/2-b=0
b=5/2
plug this into the second equation to find h
5/2+h=5
h=5-5/2=5/2
so...b=2.5 and h=2.5

Answer 2

thank you!