Question

triangle klm is similar to triangle nop. find the measure of side pn. figures are not drawn to scale.

Explanation:

Step1: Set up the proportion

Since the triangles are similar, the ratios of corresponding sides are equal. So, $\frac{MK}{PN}=\frac{ML}{PO}$.

Step2: Substitute the known values

We know $MK = 2$, $ML = 3$, and $PO=6.9$. Substituting these into the proportion gives $\frac{2}{PN}=\frac{3}{6.9}$.

Step3: Cross - multiply

Cross - multiplying gives $3\times PN=2\times6.9$.

Step4: Solve for $PN$

First, calculate $2\times6.9 = 13.8$. Then, $PN=\frac{13.8}{3}$.

Answer:

$4.6$