Question

in the diagram below, (overline{qr}) is parallel to (overline{no}). if (qr = 30), (po = 28), and (pr = 20), find the length of (overline{no}). figures are not necessarily drawn to scale.

Explanation:

Step1: Identify similar triangles

Since $\overline{QR} \parallel \overline{NO}$, $\triangle QRP \sim \triangle NOP$ by AA similarity (corresponding angles are equal due to parallel lines and transversals).

Step2: Set up proportion of sides

For similar triangles, corresponding sides are proportional:
$\frac{QR}{NO} = \frac{PR}{PO}$

Step3: Substitute known values

Substitute $QR=30$, $PR=20$, $PO=28$:
$\frac{30}{NO} = \frac{20}{28}$

Step4: Solve for $NO$

Cross-multiply and isolate $NO$:
$NO = \frac{30 \times 28}{20}$
$NO = 42$

Answer:

42