Question

style 1: the similar triangles are two separate triangles. find x: create a proportion matching the corresponding sides. two possible answers:

Explanation:

Step1: Identify corresponding sides

Since the triangles are similar, the sides \( AB = 10 \), \( BC = 6 \), \( EF = 12 \), and \( DE = x \) are corresponding. So the proportion is \( \frac{AB}{DE}=\frac{BC}{EF} \), which is \( \frac{10}{x}=\frac{6}{12} \).

Step2: Cross - multiply to solve for \( x \)

Cross - multiplying the proportion \( \frac{10}{x}=\frac{6}{12} \), we get \( 6x = 10\times12 \).

Step3: Calculate the value of \( x \)

First, calculate \( 10\times12 = 120 \). Then, solve for \( x \) by dividing both sides of the equation \( 6x = 120 \) by 6: \( x=\frac{120}{6}=20 \).

Answer:

\( x = 20 \)