Final answer:
To find the value of mn, we compare the ratios of corresponding side lengths in similar triangles. By setting up an equation and solving for mn, we find that mn = 30 cm.
Step-by-step explanation:
To find the value of mn, we first need to determine the scale factor between the similar triangles ABCD and LMNO. The ratio of corresponding side lengths in similar triangles is equal to the scale factor. Using the given information, we have:
AB/BC = LM/NO
Substituting the given values, we get:
18/14.4 = 24/mn
Cross multiplying and solving for mn, we get:
mn = (18 * mn) / 14.4 = 18 * 24 / 14.4 = 30 cm
Therefore, the value of mn is 30 cm (option d).