Science:Math Exam Resources/Courses/MATH102/December 2011/Question 09/Statement

Consider the isosceles triangle given in the following figure, where a and b indicate the side lengths. Assume that the triangle has a circumference of 2. Find the lengths a and b for which the area A of the triangle is maximized. You must also check that you found a maximum and your solution must include that check. Hint: Heron's formula may be useful which states that

$A^{2}=s(s-x)(s-y)(s-z)$

where A is the area of the triangle, x, y, z are its side lengths and s = (x+y+z)/2.