Question

3 - 74. solve for the missing lengths in the sets of similar figures below. a. $\triangle abcsim\triangle opq$

Explanation:

Step1: Set up the proportion

For similar triangles $\triangle ABC\sim\triangle OPQ$, the ratios of corresponding sides are equal. So, $\frac{AB}{PQ}=\frac{BC}{OQ}$. Here, $AB = 4$, $BC = 6$, and $PQ=6$. Let $OQ = f$. The proportion is $\frac{4}{6}=\frac{6}{f}$.

Step2: Cross - multiply

Cross - multiplying the proportion $\frac{4}{6}=\frac{6}{f}$ gives us $4f=6\times6$.

Step3: Solve for $f$

We have $4f = 36$. Dividing both sides by 4, we get $f=\frac{36}{4}=9$.

Answer:

9