Question

An isosceles triangle has sides of length x, x, and y. in addition, assume the triangle has perimeter 24. (a) find the rule for a function that computes the area of the triangle as a function of x.

Answer 1

A(x) = (24 -2x)√(6(x -6))

Explanation:

Heron's formula for the area of a triangle in terms of sides a, b, and c is ...

A = √(s(s -a)(s -b)(s -c))

where s is the semi-perimeter.

Here, we have s = 24/2 = 12, and a = b = x, c = 24-2x. So, the area is ...

A = √(12(12 -x)(12 -x)(12 -(24 -2x)) = (12 -x)√(12(2x -12))

A = 2(12 -x)√(6(x -6))