Question

MN is parallel to XZMN is 6 units. Find the lengths of NZ and XZ.

Answer 1

Since these triangles are similar, we can express the ratios of their sides like this:

$\frac{YX}{YM}=\frac{YZ}{YN}=\frac{XZ}{NM}$

By taking the first two ratios replacing the known values and then solving for YZ, we get:

$\begin{gathered} \frac{YX}{YM}=\frac{YZ}{YN} \\ \frac{YZ}{3}=\frac{10}{5} \\ \frac{YZ}{3}=2 \\ YZ=2\times3=6 \end{gathered}$

The length of NZ is the length of YZ minus the length of YN:

NZ=YZ-YN=6-3=3

Then, NZ equals 3

By taking the last two ratios we can calculate XZ, like this:

$\begin{gathered} \frac{YZ}{YN}=\frac{XZ}{NM} \\ \frac{6}{3}=\frac{XZ}{6} \\ \frac{XZ}{6}=\frac{6}{3} \\ \frac{XZ}{6}=2 \\ XZ=2\times6 \\ XZ=12 \end{gathered}$

Then, XZ equals 12