Question

given: $overline{pq}paralleloverline{hi}$. find the length of $overline{gh}$.
a 23
b 26
c 28
d 30

Explanation:

Step1: Identify similar triangles

Since $\overline{PQ}\parallel\overline{HI}$, $\triangle GPQ\sim\triangle GHI$ by the AA (angle - angle) similarity criterion (corresponding angles are equal).

Step2: Set up proportion

The ratios of corresponding sides of similar triangles are equal. So, $\frac{GP}{GH}=\frac{GQ}{GI}$. Let $GH = x$. Then $\frac{10}{x}=\frac{15}{15 + 24}$.

Step3: Cross - multiply

Cross - multiplying gives $15x=10\times(15 + 24)$.

Step4: Simplify right - hand side

$10\times(15 + 24)=10\times39 = 390$. So, $15x = 390$.

Step5: Solve for x

Dividing both sides by 15, we get $x=\frac{390}{15}=26$.

Answer:

B. 26