Question

7. Triangle MNQ is similar to triangle MOP. N 30 cm 9 cm M 0 12 cm P M M 24 cm Find the length of NQ. O A. 9.6 cm O B. 15 cm O C. 60 cm O D. 22.5 cm Please help!!! :( It is due today !!!

Answer 1

If the triangles MNQ and MOP are similar, then you know that the corresponding sides are at the same ratio. Because of this property, we can determine that:

$\frac{MN}{MO}=\frac{MQ}{MP}=\frac{NQ}{OP}$

We know the measure of the corresponding sides MQ=12cm and MO=24cm, and the measure of the corresponding side to NQ, using these measures we can calculate NQ as follows:

$\begin{gathered} \frac{MQ}{MO}=\frac{NQ}{OP} \\ \frac{12}{24}=\frac{x}{30} \\ 30(\frac{12}{24})=x \\ x=15 \end{gathered}$

Side NQ measures 15 cm

The correct option is B.