Question

△def ~ △xyz. what is xz? (not drawn to scale) a 12 b 16 c 7 d 6

Explanation:

Step1: Recall similarity - side ratio property

For similar triangles $\triangle DEF\sim\triangle XYZ$, the ratios of corresponding sides are equal. Let's assume the ratio of corresponding sides is based on the pair of sides with known lengths. If we assume $XY$ corresponds to $DE$ and $XZ$ corresponds to $DF$.

Step2: Set up the proportion

We know that $\frac{XY}{DE}=\frac{XZ}{DF}$. Given $XY = 4$, $DE=16$, and $DF = 28$. Substituting the values into the proportion: $\frac{4}{16}=\frac{XZ}{28}$.

Step3: Solve for $XZ$

Cross - multiply: $16\times XZ=4\times28$. Then $16XZ = 112$. Divide both sides by 16: $XZ=\frac{112}{16}=7$.

Answer:

C. 7