Question

the two triangles are similar. what is the value of x? enter your answer in the box. x =

Explanation:

Step1: Set up proportion

Since the two triangles are similar, the ratios of their corresponding sides are equal. We have the proportion $\frac{2x - 2}{3x}=\frac{8}{6 + 8}$.

Step2: Simplify the right - hand side

Simplify $\frac{8}{6+8}=\frac{8}{14}=\frac{4}{7}$. So our equation becomes $\frac{2x - 2}{3x}=\frac{4}{7}$.

Step3: Cross - multiply

Cross - multiplying gives us $7(2x - 2)=4\times3x$.

Step4: Expand the left - hand side

Expand $7(2x - 2)$ to get $14x-14 = 12x$.

Step5: Solve for x

Subtract $12x$ from both sides: $14x-12x-14=0$, which simplifies to $2x-14 = 0$. Then add 14 to both sides: $2x=14$. Divide both sides by 2: $x = 7$.

Answer:

$7$