One of the legs of a right-angled triangle is 5cm larger than the other, and the sum of the legs is 19cm.

Let the first leg of a right-angled triangle be less than and equal to x centimeters. Then the second rolls of this triangle will be equal to (x + 5) centimeters. According to the condition, it is said that the sum of the legs is 19 centimeters. Therefore, we can draw up an equation from which we find the lengths of both legs.

The resulting equation:

x + (x + 5) = 19;

2x + 5 = 19;

2x = 14;

x = 7 (cm) – the first leg.

Then the second leg:

7 + 5 = 12 (cm).

Answer: The first leg of the triangle is 7 centimeters, the second leg is 12 centimeters.