Question

for the pair of similar triangles, find the appropriate value(s) of x. the appropriate value(s) of x is/are \boxed{}. (simplify your answer. use a comma to separate answers as needed.)

Explanation:

Step1: Set up proportion for similar triangles

Corresponding sides of similar triangles are proportional: $\frac{2x-6}{x+8} = \frac{39}{20}$

Step2: Cross-multiply to eliminate fractions

$20(2x-6) = 39(x+8)$

Step3: Expand both sides of the equation

$40x - 120 = 39x + 312$

Step4: Isolate x on one side

$40x - 39x = 312 + 120$

Step5: Calculate final value of x

$x = 432$

Answer:

$432$