The number of right triangles satisfying that the lengths of two right angles are integers and the perimeter is exactly equal to the integral multiple of the area is ()

Let two right angle sides be a and B, then the oblique side length is √ (a ^ 2 + B ^ 2) √ which means root sign
Perimeter = a + B + √ (a ^ 2 + B ^ 2)
Area = 1 / 2 * a * B
It is necessary to satisfy that the lengths of the two right angles are integers, and the perimeter is exactly equal to the integral multiple of the area
So √ (a ^ 2 + B ^ 2) must be an integer
The square of an integer can be decomposed into the sum of the squares of the other two integers. Only 3, 4, 5 and their integral multiples of Pythagorean theorem are satisfied. In addition, the perimeter is just equal to the integral multiples of area, so only 3, 4, 5 and 6, 8, 10 can be satisfied
So the final answer should be two

What is the area of a right triangle whose three sides are integers and whose perimeter is equal to 30?
I know the answer, can give detailed process as far as possible
The topic requests to prove with Pythagorean theorem
I don't know how to prove it

C is the largest edge, so: C > (a + B + C) / 3 > 10
And a + b > C, so: C

The length of the three sides of a right triangle is an integer, and the perimeter value is equal to the area. How to find the length of the three sides? (the process should be complete)

Let the right angle side be a, B. from the question meaning: AB / 2 = a + B + √ (a ^ 2 + B ^ 2) and the transformation of the square, we can get: A ^ 2B ^ 2 / 4 + 2Ab AB (a + b) = 0, because AB is not equal to 0, so a + b-ab / 4 = 2

The number of right triangles satisfying that the lengths of two right angles are integers and the perimeter is exactly equal to the integral multiple of the area is ()