My maths teacher gave me some problems and one of them was that I have a right triangle with side 6 and area 30.. So my questions are: 1.Is this even possible and 2.should I assume that most of the time, a right triangle with side 6 would be egyptian (pythagorean triple) P.S sorry if my sentence formation isn't top tier..
The side of length 6 is a cathetus (adjacent to right angle): As the area is $30 = \frac12 c\cdot6$ where $c$ is the length of the other cathetus, there must be $c=10$.
The side of length 6 is the hypothenuse (opposite of right angle): The area is $30=\frac12h\cdot6$ where $h$ is the height of the triangle, thus $h = 10$. Moreover, as it is a right triangle, the right angle is at Thales' circle which has radius $6/2 = 3$ around the middle of the hypothenuse. As this circle does not intersect a line that is $h=10$ units away from the hypothenuse and parallel to it, no solutions from this case.