Question

in the diagram below, $\triangle abc\sim \triangle dec$. what is the value of $x$?\
\
a. 2\
b. 3.5\
c. 3\
d. 2.5

Explanation:

Step1: Set up similarity proportion

Since $\triangle ABC \sim \triangle DEC$, corresponding sides are proportional:
$\frac{x}{18-x} = \frac{5}{25}$

Step2: Simplify the ratio

Simplify $\frac{5}{25}$ to $\frac{1}{5}$:
$\frac{x}{18-x} = \frac{1}{5}$

Step3: Cross-multiply to solve for x

Cross-multiply to eliminate fractions:
$5x = 18 - x$

Step4: Isolate x term

Add $x$ to both sides:
$5x + x = 18$
$6x = 18$

Step5: Solve for x

Divide both sides by 6:
$x = \frac{18}{6} = 3$

Answer:

C. 3