Find the hypotenuse of a right-angled triangle if one of its legs is 3 cm, and the radius of the inscribed circle is 1 cm.

According to the formula, the radius is calculated (r) = (a + b – c) / 2, where a = 3 cm and b – legs, r = 1 cm.Let’s find side c – hypotenuse.

1 = (3 + b – c) / 2.

1 * 2 = 3 + b – c.

2 – 3 = b – c.

– 1 = b – c.

– c = –1 – b.

c = 1 + b.

Let’s apply the Pythagorean theorem:

(b + 1) ² = 3² + b².

b² + 2 * 1 * b + 1 = 9 + b².

2b + 1 = 9.

2b = 9 – 1.

2b = 8.

b = 4.

c = 4 + 1 = 5 cm.

Solution: hypotenuse – 5 cm.