Question

what is the greatest possible are of a triangle with one side of length 7 and another side of length 10?

Answer 1

Area of a triangle = $\frac{1}{2} (a)(b)sin(C)$.

a=7
b=10

The largest possible value for sin(C) is 1, which is sin(90)

So area = $\frac{1}{2} (7)(10)sin(90) = \frac{1}{2} (7)(10)(1) =35$