Question

the following figures are similar. solve for the variables. include proportion
27)
28)

Explanation:

Step1: Set up proportion for problem 27

Since the triangles are similar, the ratio of corresponding sides is equal. So, \(\frac{u}{3}=\frac{14}{21}\)

Step2: Solve for \(u\)

Cross - multiply: \(21u = 3\times14\), then \(21u=42\), divide both sides by 21: \(u=\frac{42}{21}=2\)

Step3: Set up proportion for problem 28 (assuming \(\triangle ABC\sim\triangle XYZ\))

If \(\frac{AB}{XY}=\frac{BC}{YZ}=\frac{AC}{XZ}\), then \(\frac{4}{3}=\frac{a}{4.5}\)

Step4: Solve for \(a\)

Cross - multiply: \(3a = 4\times4.5\), then \(3a = 18\), divide both sides by 3: \(a = 6\)

Also, \(\frac{AC}{XZ}=\frac{3.2}{y}=\frac{4}{3}\)
Cross - multiply: \(4y=3.2\times3\), then \(4y = 9.6\), divide both sides by 4: \(y = 2.4\)

Answer:

For problem 27: \(u = 2\)
For problem 28: \(a = 6\), \(y=2.4\)