Question

question 9 of 10
what is the length of \\( \overline { c d } \\) ? in this diagram, \\( \delta a b c \sim \delta e d c \\).

a. 3
b. 5
c. 4
d. 2

Explanation:

Step1: Use Similar Triangles Proportion

Since $\triangle ABC \sim \triangle EDC$, the corresponding sides are proportional. So, $\frac{AC}{EC} = \frac{BC}{DC}$. We know $AC = 20$, $EC = 5$, $BC = 20 - x$, and $DC = x$. Substituting these values, we get $\frac{20}{5} = \frac{20 - x}{x}$.

Step2: Solve the Proportion

Simplify $\frac{20}{5}$ to $4$, so the equation becomes $4 = \frac{20 - x}{x}$. Cross - multiply: $4x = 20 - x$. Add $x$ to both sides: $4x + x = 20$, which is $5x = 20$. Divide both sides by $5$: $x=\frac{20}{5}=4$.

Answer:

C. 4