5. A triangular area must be enclosed by a fence 80 feet long. What dimensions will maximize the area?

Answer 1

80/3 by 80/3 by 80/3

or

about 26.7 by 26.7 by 26.7 feet

or 26 2/3 by 26 2/3 by 26 2/3 or .

actually 26.666... by 26.666.. by 26.666....

a triangle with maximum area is an equilateral triangle with all 3 sides equal.

or try this another way

3 sides. where area of a triangle = bh/2 with b = base =one side, height = bsq3.

b = 80/2 = 40. area = 40(40sqr3)/2 = 800sqr3 = about 80(1.732) = about 138.6 = max area