Question

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

Explanation:

Step1: Set up proportion

Since $\triangle ABC\sim\triangle DEC$, the ratios of corresponding sides are equal. So, $\frac{AB}{DE}=\frac{BC}{EC}$. Substituting the given values, we get $\frac{x}{18 - x}=\frac{5}{25}$.

Step2: Cross - multiply

Cross - multiplying the proportion $\frac{x}{18 - x}=\frac{5}{25}$ gives $25x=5(18 - x)$.

Step3: Expand right - hand side

Expanding $5(18 - x)$ gives $25x = 90-5x$.

Step4: Add $5x$ to both sides

Adding $5x$ to both sides of the equation $25x = 90-5x$ gives $25x+5x=90$, which simplifies to $30x = 90$.

Step5: Solve for $x$

Dividing both sides of $30x = 90$ by 30, we get $x=\frac{90}{30}=3$.

Answer:

C. 3