Final answer:
By applying the Pythagorean theorem to the condition that a right-angled triangle's area equals its perimeter, we can look for integer solutions that satisfy this equation to find the required triangles.
Step-by-step explanation:
To find all right-angled triangles with integer side lengths whose area equals their perimeter, we can use the Pythagorean theorem. The legs of the triangle are denoted by a and b, and the hypotenuse by c. The theorem states that a² + b² = c². For a right-angled triangle, the area (A) can be expressed as (a*b)/2, and the perimeter (P) as a + b + c. We are looking for integer solutions where A = P.