Question

the triangles in the following are similar. find the length x rounded to the nearest tenth
9)
10)
11)
12)

Explanation:

Step1: Set up proportion for similar triangles

For similar triangles, the ratios of corresponding sides are equal. For the first pair (problem 9), we have \(\frac{x}{6}=\frac{6}{4}\).

Step2: Solve for \(x\)

Cross - multiply: \(4x = 6\times6\), so \(4x=36\), then \(x=\frac{36}{4}=9.0\).

For problem 10 (assuming the proportion \(\frac{x}{4}=\frac{9}{3}\)):

Step1: Set up proportion

\(\frac{x}{4}=\frac{9}{3}\)

Step2: Solve for \(x\)

Cross - multiply: \(3x = 4\times9\), \(3x = 36\), \(x = 12.0\)

For problem 11 (assuming the proportion \(\frac{x}{5}=\frac{10}{2}\)):

Step1: Set up proportion

\(\frac{x}{5}=\frac{10}{2}\)

Step2: Solve for \(x\)

Cross - multiply: \(2x=5\times10\), \(2x = 50\), \(x = 25.0\)

Answer:

1. \(x = 9.0\)
2. \(x = 12.0\)
3. \(x = 25.0\)