In a right-angled triangle, one leg is 7 cm. Determine the other two integer sides.

Let us denote the legs of this right-angled triangle by a and b,

and its hypotenuse through c.

By the condition of the problem, it is known that one of the legs is 7 cm long.

Let it be leg b = 7 cm.

By the Pythagorean theorem for a given right-angled triangle we have:

a ^ 2 + b ^ 2 = c ^ 2,

a ^ 2 + 7 ^ 2 = c ^ 2,

c ^ 2 – a ^ 2 = 7 ^ 2,

(c – a) * (c + a) = 7 ^ 2.

We need to find whole solutions to the last equation.

Obviously, the factor (c – a) can be either 1, or 7, or 49.

Since c – a <c + a, then c – a cannot be equal to 7 and 49.

Therefore, we have:

c – a = 1,

c + a = 49.

Let us add both equations:

(c – a) + (c + a) = 1 + 49,

2 * c = 50,

c = 25. Hence, a = 49 – c = 49 – 25 = 24.

So, we got that the legs are 24 and 7, and the hypotenuse is 25.