Rationalize This

Find the a right triangle with rational side lengths, and a hypotenuse numerically equal to the area of the triangle.


A rational right triangle is a triangle where all the sides are rational numbers and one of the angles is a right angle.
Find a rational right triangle such that the length of the hypotenuse is numerically equal to the area of the triangle, and the perimeter of the triangle is a prime integer.

(Source: Greg Weidman)