Question

question 1 of 10
what is the length of \\( \overline { d e } \\)?

a. 5
b. 6
c. 7
d. 8

Explanation:

Step1: Determine similarity of triangles

Since \(\triangle XYZ\) and \(\triangle DEF\) have two sides in proportion (\(\frac{12}{8}=\frac{3}{2}\)) and the included angle equal (\(44^{\circ}\)), by the Side - Angle - Side (SAS) similarity criterion, \(\triangle XYZ\sim\triangle DEF\).

Step2: Set up proportion

For similar triangles, the ratios of corresponding sides are equal. So \(\frac{XY}{DE}=\frac{XZ}{DF}\). Substituting the known values: \(\frac{9}{x}=\frac{12}{8}\).

Step3: Solve the proportion

Cross - multiply: \(12x = 9\times8\). Then \(12x=72\). Divide both sides by 12: \(x=\frac{72}{12}=6\).

Answer:

B. 6