Question

1. in the diagram below, $overline{op}$ is parallel to $overline{lm}$. if $lm = 21$, $np = 8$, and $mp = 6$, find the length of $overline{op}$. figures are not necessarily drawn to scale.

Explanation:

Step1: Calculate length of MN

$MN = MP + NP = 6 + 8 = 14$

Step2: Set up similarity proportion

Since $\overline{OP} \parallel \overline{LM}$, $\triangle NOP \sim \triangle NLM$. So $\frac{OP}{LM} = \frac{NP}{MN}$

Step3: Substitute values and solve for OP

$\frac{OP}{21} = \frac{8}{14}$
$OP = 21 \times \frac{8}{14}$
$OP = 12$

Answer:

$12$