Question

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in δmno, \\(\overline{mn} \parallel \overline{pq}\\). given that \\(om = 32\\), \\(op = 20\\), and \\(mn = 40\\), find \\(pq\\).

Explanation:

Step1: Set up similarity proportion

Since $\overline{MN} \parallel \overline{PQ}$, $\triangle OMN \sim \triangle OPQ$, so $\frac{OP}{OM} = \frac{PQ}{MN}$

Step2: Substitute given values

$\frac{20}{32} = \frac{PQ}{40}$

Step3: Solve for $PQ$

$PQ = 40 \times \frac{20}{32} = 40 \times \frac{5}{8}$

Answer:

25