Question

triangles abc and def are similar triangles. use this fact to solve the exercise. round to the nearest tenth. find side de (in inches).

Explanation:

Step1: Identify corresponding sides

Since $\triangle ABC \sim \triangle DEF$, the corresponding sides are proportional. So, $\frac{AB}{DE}=\frac{BC}{EF}$. We know $AB = 8$ in, $BC = 9$ in, and $EF = 14$ in.

Step2: Set up proportion and solve for DE

Substitute the known values into the proportion: $\frac{8}{DE}=\frac{9}{14}$. Cross - multiply to get $9\times DE=8\times14$. Then $DE=\frac{8\times14}{9}$.
Calculate $8\times14 = 112$, so $DE=\frac{112}{9}\approx12.4$ (rounded to the nearest tenth).

Answer:

12.4