Question

given: $overline{pq}paralleloverline{hi}$. find the length of $overline{gh}$.

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 $GP = 10$, $GQ = 15$, $GI=15 + 24=39$, and $GH=10 + PH$.
The proportion is $\frac{10}{x}=\frac{15}{15 + 24}$.

Step2: Cross - multiply

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

Step3: Solve for $x$

$15x = 390$, so $x=\frac{390}{15}=26$.

Answer:

B. 26