Question

solve for x. the triangles in each pair are similar.
17)
18)
19)
20)

Explanation:

Step1: Set up the proportion for similar triangles

Since the triangles are similar, the ratios of corresponding sides are equal. For problem 17, we have \(\frac{70}{60}=\frac{11x - 4}{50}\).

Step2: Cross - multiply

Cross - multiplying gives \(70\times50=60\times(11x - 4)\).

Step3: Simplify the equation

\(3500 = 660x-240\).

Step4: Solve for \(x\)

Add 240 to both sides: \(3500 + 240=660x\), so \(3740 = 660x\). Then \(x=\frac{3740}{660}=\frac{17}{3}\approx5.67\).

For problem 18, \(\frac{77}{30}=\frac{11x + 11}{21}\). Cross - multiplying: \(77\times21 = 30\times(11x + 11)\). \(1617=330x + 330\). Subtract 330: \(1617-330 = 330x\), \(1287 = 330x\), \(x=\frac{1287}{330}=\frac{39}{10}=3.9\).

For problem 19, \(\frac{27}{72}=\frac{- 4 + 4x}{64}\). Cross - multiplying: \(27\times64=72\times(-4 + 4x)\). \(1728=-288 + 288x\). Add 288: \(1728 + 288=288x\), \(2016 = 288x\), \(x = 7\).

For problem 20, \(\frac{88}{24}=\frac{5x + 11}{18}\). Cross - multiplying: \(88\times18=24\times(5x + 11)\). \(1584 = 120x+264\). Subtract 264: \(1584 - 264=120x\), \(1320 = 120x\), \(x = 11\).

Answer:

1. \(x=\frac{17}{3}\)
2. \(x = 3.9\)
3. \(x = 7\)
4. \(x = 11\)