TITLE: Area triangle (possible)
QUESTION [5 upvotes]: The area of a right triangle is an integer greater than $ 85 $. If the hypotenuse measures $ 20 $, what is the area of this triangle?
It’s just a 3-4-5 right triangle, so the area is $\boxed{96}$.
This is true? If so, how to prove it?
But he said the area is integer, not the sides
Can you use Weitzenbock inequality in this problem?

REPLY [6 votes]: The area of the right triangle with hypotenuse $|AB|=20$
can be any real number in a range  $(0,100]$, 
so if the only limiting condition is that it must be an integer greater than $85$,
the answer is that it could be any integer $n$ from $86$ to $100$.