Question

1. 30 ft 25 ft 30 ft x = 3) 15 yd 10 yd x 18 yd x = 4) 6 cm. 2 cm. 1 cm. x = 5) 3 m. 2 m. 6 m. x

Explanation:

2)

Step1: Set up proportion

Since the triangles are similar, the ratios of corresponding sides are equal. So, \(\frac{20}{x}=\frac{25}{30}\).

Step2: Cross - multiply

Cross - multiplying gives \(25x = 20\times30\).

Step3: Solve for \(x\)

\(25x=600\), then \(x=\frac{600}{25}=24\).

3)

Step1: Set up proportion

For the similar triangles, \(\frac{15}{18}=\frac{10}{x}\).

Step2: Cross - multiply

Cross - multiplying gives \(15x = 18\times10\).

Step3: Solve for \(x\)

\(15x = 180\), then \(x=\frac{180}{15}=12\).

4)

Step1: Set up proportion

For the similar triangles, \(\frac{x}{1}=\frac{6}{2}\).

Step2: Solve for \(x\)

Since \(\frac{6}{2}=3\), then \(x = 3\).

5)

Step1: Set up proportion

For the similar triangles, \(\frac{3}{x}=\frac{2}{6}\).

Step2: Cross - multiply

Cross - multiplying gives \(2x=3\times6\).

Step3: Solve for \(x\)

\(2x = 18\), then \(x=\frac{18}{2}=9\).

Answer:

1. \(x = 24\)
2. \(x = 12\)
3. \(x = 3\)
4. \(x = 9\)