Question

b. efghi ~ stuvw
c. jklm ~ wxyz

Explanation:

1. For similar - polygons \(EFGHI\sim STUVW\):

• When two polygons are similar, the ratios of their corresponding side - lengths are equal. Let's assume we want to find the ratio of similarity.
• The ratio of the corresponding sides \(EF\) and \(ST\) is \(\frac{EF}{ST}=\frac{24}{20}=\frac{6}{5}\). The ratio of the corresponding sides \(GH\) and \(UV\) should also be the same. Let's check: \(\frac{GH}{UV}=\frac{8}{15}

eq\frac{6}{5}\). There seems to be an error in the problem statement if we assume we are looking for the ratio of similarity or missing information. But if we assume we want to find a missing side - length based on the similarity ratio.

• Let's say we want to find a side of \(EFGHI\) given a side of \(STUVW\) or vice - versa. The ratio of similarity \(k=\frac{EF}{ST}=\frac{6}{5}\).

1. For similar polygons \(JKLM\sim WXYZ\):

• Since the two polygons are similar, the ratios of their corresponding side - lengths are equal. Let the ratio of similarity be \(k\).
• We know that if we consider the ratio of the vertical sides, \(k = \frac{ML}{ZY}=\frac{3}{10}\).
• If we want to find the length of \(WZ\) (corresponding to \(MJ\)) using the ratio of similarity. Let \(MJ = 7\) and \(WZ=h\).
• The ratio of similarity \(k=\frac{3}{10}\), and we can set up the proportion \(\frac{MJ}{WZ}=\frac{3}{10}\). Substituting the values, we have \(\frac{7}{h}=\frac{3}{10}\).
• Cross - multiply to get \(3h = 70\).
• Solve for \(h\):
• \(h=\frac{70}{3}\).

Step1: Identify the ratio of similarity for \(JKLM\sim WXYZ\)

Set the ratio of the known corresponding vertical sides \(\frac{ML}{ZY}=\frac{3}{10}\)

Step2: Set up a proportion for the unknown side

Let \(MJ = 7\) and \(WZ = h\), then \(\frac{MJ}{WZ}=\frac{3}{10}\), so \(\frac{7}{h}=\frac{3}{10}\)

Step3: Cross - multiply

We get \(3h = 70\)

Step4: Solve for \(h\)

\(h=\frac{70}{3}\)

Answer:

For the similar polygons \(JKLM\sim WXYZ\), if \(MJ = 7\), \(ML = 3\), \(ZY = 10\), the length of \(WZ\) is \(\frac{70}{3}\)