Question

nament according to the words under each answer.
abcde ~ vwxyz

1. find the length

of dc.

1. find the length of vw.

cat ~ dog

1. find the length of od.
2. find the length of ct.

(images of similar polygons: pentagons abcde and vwxyz, triangles cat and dog with labeled side lengths)

Explanation:

Step1: Determine the scale factor for ABCDE ~ VWXYZ

Since \(DE = 2\) and \(ZY=5\), the scale factor \(k=\frac{ZY}{DE}=\frac{5}{2}\)

Step2: Find the length of \(DC\)

We know that \(XY = 8\). Using the similarity of polygons \(ABCD E\sim VWXYZ\), and the ratio of corresponding sides. Let \(DC=x\). The ratio of corresponding sides gives \(\frac{XY}{DC}=\frac{5}{2}\). Substituting \(XY = 8\) into \(\frac{8}{x}=\frac{5}{2}\), we can cross - multiply: \(5x=16\), so \(x=\frac{16}{5}=3.2\)

Step3: Determine the scale factor for CAT ~ DOG

Since \(AG = 66\) and \(AT = 30\), the scale factor \(k=\frac{AG}{AT}=\frac{66}{30}=\frac{11}{5}\)

Step4: Find the length of \(OD\)

We know that \(CA = 24\). Let \(OD = y\). Using the similarity of triangles \(CAT\sim DOG\), and the ratio of corresponding sides \(\frac{OD}{CA}=\frac{11}{5}\). Substituting \(CA = 24\) into \(\frac{y}{24}=\frac{11}{5}\), cross - multiply: \(5y=264\), so \(y = 52.8\)

Answer:

1. The length of \(DC\) is \(3.2\)
2. The length of \(OD\) is \(52.8\)