Area S of triangle with sides a, b and c and with perimeter a+b+c=2*p is
The area of the triangle will be the largest when (p-a)(p-b)(p-c) is maximum.
Notice, that the sum of each term in that product is constant.
(p-a)(p-b)(p-c) => p-a + p-b + p-c = 3*p -(a+b+c)= 3p-2p=p
We conclude what sum will be largest when a=b=c. In other words, equilateral triangle has the largest area.
Back to Geometry Problems