What is the reason behind this SAT Math Question?

MyRealName
Thu, 01 Aug 2013 22:07:09 +0000

What is the greatest possible area of a triangle with
one side of length 7 and another side of length 10?
(A) 17
(B) 34
(C) 35
(D) 70
(E) 140

The answer is choice C, and I know how to get it, but I’m wondering why the answer can’t be 80? It can be proposed that a third side is 16 (a + b > c, 10 + 17 > 16) and then the largest side would be .5 x (5) x 16 or .5 x (7) x 16, which are both 80.