Question

triangle abc is similar to triangle def. the following ratios of corresponding sides are equal.
\frac{8}{12}=\frac{16}{24}=\frac{2x + 5}{2x + 11}
x=\frac{7}{2}
(type an integer or a simplified fraction.)
side ac = 12.
(type an integer or decimal rounded to the nearest tenth.)
side df=
(type an integer or decimal rounded to the nearest tenth.)

Explanation:

Step1: Use the ratio equality

Since $\frac{8}{12}=\frac{16}{24}=\frac{2x + 5}{2x+11}$, and we know $x=\frac{7}{2}$.

Step2: Find side DF

Substitute $x = \frac{7}{2}$ into the expression for side DF which is $2x + 11$. So $2\times\frac{7}{2}+11=7 + 11=18$.

Answer:

18