Final answer:
To find the length of AB in similar triangles ABC and LMN with given perimeters, we can use proportions. Setting up a proportion and solving for AB gives us a length of 10 cm.
Step-by-step explanation:
To find the length of AB, we can use the fact that the triangles ABC and LMN are similar. Similar triangles have proportional side lengths. So, if the perimeter of ABC is 60 cm and the perimeter of LMN is 48 cm, the ratios of corresponding side lengths are equal.
Let's set up a proportion using the lengths of AB and LM:
AB/LM = (Perimeter of ABC)/(Perimeter of LMN)
AB/8 = 60/48
Next, we can cross multiply and solve for AB:
AB = (8 * 60) / 48
AB = 10 cm