Question

triangle rst is similar to triangle rvw. what is the value of d in millimeters?

Explanation:

Step1: Identify the ratio of corresponding sides

Since $\triangle RST\sim\triangle RVW$, the ratio of the corresponding sides is equal. The ratio of the vertical sides is $\frac{RW}{RT}=\frac{10}{10 + 5}=\frac{10}{15}=\frac{2}{3}$.

Step2: Set up proportion for horizontal sides

Let the ratio of the horizontal sides be the same as the ratio of the vertical sides. We have $\frac{d}{18}=\frac{2}{3}$.

Step3: Solve for $d$

Cross - multiply: $3d=18\times2$. Then $3d = 36$, and $d=\frac{36}{3}=12$.

Answer:

12