The area of a right-angled triangle is 12 cm ^ 2, and one of its legs is 6 cm. Find the hypotenuse of the triangle.

The area of a right-angled triangle is calculated by the formula:
S = 1/2 * ab,
where S is the area of a right-angled triangle, a and b are legs.
Substitute the known values into the formula:
12 = 1/2 * 6b.
Let’s solve the resulting equation:
12 = 6b / 2;
12 = 3b;
b = 12/3;
b = 4.
Knowing the two legs of a right-angled triangle, we find its hypotenuse by the Pythagorean theorem:
c ^ 2 = a ^ 2 + b ^ 2;
c = √ (a ^ 2 + b ^ 2);
c = √ (6 ^ 2 + 4 ^ 2) = √ (36 + 16) = √52 = √ (4 * 13) = 2√13 (cm).
Answer: c = 2√13 cm.