Question

question 3 of 10
what is the length of $overline{de}$?
a. 9
b. 15
c. 6
d. 10

Explanation:

Step1: Identify similar triangles

Triangles $\triangle ABC$ and $\triangle DEF$ are similar (SAS similarity: $\angle C = \angle F = 49^\circ$, and $\frac{AC}{DF} = \frac{BC}{EF}$).

Step2: Set up proportion

$\frac{AB}{DE} = \frac{BC}{EF}$
Substitute values: $\frac{15}{x} = \frac{18}{12}$

Step3: Solve for $x$

Simplify $\frac{18}{12} = \frac{3}{2}$, so $\frac{15}{x} = \frac{3}{2}$
Cross multiply: $3x = 15 \times 2$
$3x = 30$
$x = \frac{30}{3} = 10$

Answer:

D. 10