For right-angled triangles, the sum of the legs is 7 cm, and the difference between the legs is 1 cm.

For right-angled triangles, the sum of the legs is 7 cm, and the difference between the legs is 1 cm. Find the sides of the triangle.

Let one leg be equal to a, the other leg equal to b, the hypotenuse equal to c.

Therefore, by the condition of the problem:

a + b = 7;

a – b = 1.

Since the units and coefficients in these equations are the same, this system can be solved by adding the equations.

Consequently,

2 * a = 8.

a = 4 cm.

Then, b = 7 – 4 = 3 (cm).

Using the Pythagorean theorem, we find the value of the hypotenuse.

c ^ 2 = a ^ 2 + b ^ 2 = 4 ^ 2 + 3 ^ 2 = 16 + 9 = 25.

Therefore, c = 5 (cm).

Answer: the sides of the triangle are 3 cm, 4 cm, 5 cm.