To solve this problem, we can use the concept of similarity of triangles. Similar triangles have the same shape but possibly different sizes. The ratio of corresponding sides of similar triangles is always the same.

Let's denote the lengths of the corresponding sides of the triangles as follows:
AB = x (length of side AB)
BC = y (length of side BC)
AC = z (length of side AC)
LM = 8 cm (length of side LM)
MN = p (length of side MN)
LN = q (length of side LN)

We are given that the perimeter of triangle ABC is 60 cm, so we can write the equation:
AB + BC + AC = 60
x + y + z = 60 ----(1)

We are also given that the perimeter of triangle LMN is 48 cm, so we can write the equation:
LM + MN + LN = 48
8 + p + q = 48 ----(2)

Since triangles ABC and LMN are similar, we know that the ratios of corresponding sides are equal. Therefore, we can write the proportion:
AB/LM = BC/MN = AC/LN

Dividing equation (1) by equation (2), we get:
(x + y + z)/(8 + p + q) = AB/LM

Substituting the given values, we have:
(60)/(8 + p + q) = x/8

Cross-multiplying, we get:
8x = 60(8 + p + q)

Simplifying, we have:
8x = 480 + 60p + 60q

Since LM = 8 cm, we can substitute LM with 8 in the equation:
8x = 480 + 60p + 60q

Since we are looking for the length of AB, which is x, we need to solve for x. To do this, we need more information about the triangle, such as the lengths of BC and AC, or the lengths of MN and LN. Without this additional information, we cannot determine the length of AB. Therefore, the answer cannot be determined with the given information.

Answer: Cannot be determined.

(c) 10 cm