Final answer:
To calculate the length of MN, the scale factor between the similar figures ABCD and LMNO is determined as 4/3 using sides AB and LM. This scale factor is then multiplied by side BC to find MN, which results in an MN length of 19.2 cm.option(D)
Step-by-step explanation:
To find the value of MN given that quadrilaterals ABCD and LMNO are similar (ABCD ~ LMNO), we first calculate the scale factor between the two similar figures. The scale factor is the ratio of corresponding sides in similar figures. In this case, the side LM corresponds to the side AB. Thus, the scale factor can be calculated as:
Scale factor = LM / AB = 24 cm / 18 cm = 4/3
Next, we use the scale factor to find the length of MN, which corresponds to the side BC in the smaller quadrilateral. We have:
MN / BC = Scale factor
Therefore:
MN = Scale factor × BC = (4/3) × 14.4 cm = 19.2 cm
Hence, the length of MN is 19.2 cm, which matches option d).