Question

find m.
write your answer as a whole number or a decimal. do not round.
m = meters

Explanation:

Step1: Identify similar triangles

Triangles \( \triangle QOP\) and \( \triangle NOR\) are similar. Because vertical angles are equal (\(\angle QOP=\angle NOR\)), and \(\angle QPO = \angle NRO\) (given as equal in the figure). By the AA (Angle - Angle) similarity criterion, \(\triangle QOP\sim\triangle NOR\).

Step2: Set up the proportion

For similar triangles, the ratios of corresponding sides are equal. So, \(\frac{QO}{NO}=\frac{QP}{NR}\). Let \(QO = m\), \(NO = 24\), \(QP=56\), and \(NR = 42\). Then the proportion is \(\frac{m}{24}=\frac{56}{42}\).

Step3: Solve the proportion for \(m\)

Cross - multiply: \(42m=24\times56\). First, calculate \(24\times56 = 1344\). Then, \(m=\frac{1344}{42}\). Since \(1344\div42 = 32\).

Answer:

\(32\)