given: $overline{pq}paralleloverline{hi}$. find the length of $overline{gh}$.\na 23\nb 26\nc 28\nd 30

Explanation:

Step1: Use similar - triangle property

Since $\overline{PQ}\parallel\overline{HI}$, $\triangle GPQ\sim\triangle GHI$. Then, the ratios of corresponding sides are equal. That is, $\frac{GP}{GH}=\frac{GQ}{GI}$. Let $GH = x$. We know that $GP = 10$, $GQ = 15$, and $GI=15 + 24=39$. So, $\frac{10}{x}=\frac{15}{39}$.

Step2: Cross - multiply

Cross - multiplying the proportion $\frac{10}{x}=\frac{15}{39}$ gives us $15x=10\times39$.

Step3: Solve for $x$

First, calculate $10\times39 = 390$. Then, $x=\frac{390}{15}=26$.

Answer:

B. 26