Calculate the circumference of a right-angled triangle if its area is 48 cm2 and the length of one of the legs is 6 cm.

Let us determine what value the length of the unknown leg will equal, if from the condition of our problem we know for sure that with an area of 48 cm2, the length of the known leg is 6 cm:

48 * 2: 6 = 16.

Let us determine what value will be equal to the length of the hypotenuse in this case:

√ (16 ^ 2 + 6 ^ 2) = √ (256 + 36) = √292 = 2√73.

As we know, the diameter of the circumcircle will be equal to the length of the hypotenuse, so we can calculate the length of the circumcircle:

P = πD;

3.14 * 2√73 = 6.28√73.

Answer: Circumference = 6.28√73 cm.