Question

3 as shown in the figure, abcd - a1b1c1d1, ab = 12, cd = 15, and a1b1 = 9. the length of c1d1 is __. a. 10 b. 12 c. 45/4 d. 36/5 4 among the following conditions, the one that can make △abc and △def similar is __. a. m∠c = 98°, m∠e = 98°, ac/bc = de/df b. ab = 1, ac = 1.5, bc = 2, ef = 8, de = 10, fd = 6 c. m∠a = m∠f = 90°, ac = 5, bc = 13, df = 10, ef = 26 d. m∠a = 46°, m∠b = 54°, m∠e = 54°, m∠f = 80°

Explanation:

Step1: Recall property of similar polygons

For similar polygons \(ABCD - A_1B_1C_1D_1\), the ratios of corresponding - side lengths are equal. That is, \(\frac{AB}{A_1B_1}=\frac{CD}{C_1D_1}\).

Step2: Substitute given values

We are given that \(AB = 12\), \(A_1B_1 = 9\), and \(CD = 15\). Substituting these values into the proportion \(\frac{AB}{A_1B_1}=\frac{CD}{C_1D_1}\), we get \(\frac{12}{9}=\frac{15}{C_1D_1}\).

Step3: Cross - multiply and solve for \(C_1D_1\)

Cross - multiplying gives us \(12\times C_1D_1=9\times15\). Then \(C_1D_1=\frac{9\times15}{12}=\frac{135}{12}=\frac{45}{4}\).

Answer:

C. \(\frac{45}{4}\)