Question

1. solve for the missing lengths. show all work. a. △ghi ∼ △pqr

Explanation:

Step1: Recall similarity property

For similar triangles $\triangle GHI\sim\triangle PQR$, the ratios of corresponding - sides are equal. But we need more information about which sides are corresponding. Assuming $GH$ corresponds to $PQ$ and $GI$ corresponds to $PR$. Let's say the ratio of similarity is $k$. We know that if we assume $\frac{GH}{PQ}=\frac{GI}{PR}$. However, we are missing information about which side of $\triangle GHI$ corresponds to which side of $\triangle PQR$. Let's assume $GH = 7$, $GI = 2$, and $PQ=112$.

Step2: Set up proportion

If we assume $\frac{GI}{PR}=\frac{GH}{PQ}$, substituting the known values, we have $\frac{2}{n}=\frac{7}{112}$.

Step3: Cross - multiply

Cross - multiplying gives us $7n=2\times112$.

Step4: Solve for n

First, calculate $2\times112 = 224$. Then, $n=\frac{224}{7}=32$.

Answer:

$n = 32$