Question

question 18 of 25 in the diagram below, △abc~△dec. what is the value of x? a. 2 b. 2.5 c. 3.5 d. 3

Explanation:

Step1: Set up proportion from similarity

Since $\triangle ABC \sim \triangle DEC$, corresponding sides are proportional: $\frac{AB}{DE} = \frac{BC}{EC}$.

Step2: Substitute known values

$AB = x$, $DE = 18 - x$, $BC = 5$, $EC = 25$. Thus, $\frac{x}{18 - x} = \frac{5}{25}$.

Step3: Simplify and solve for x

Simplify $\frac{5}{25} = \frac{1}{5}$. Cross-multiplying: $5x = 18 - x$. Then $6x = 18 \Rightarrow x = 3$.

Answer:

D. 3