Question

△abc ~ △def. find the value of x. diagrams of triangles abc and def with side lengths: abc has ac=32.5, bc=19.5, ab=x; def has df=10, de=8, ef=6. multiple choice options: a) 26, b) 24⅜, c) 43⅓, d) 14⅝, e) 19½

Explanation:

Step1: Identify Corresponding Sides

Since \(\triangle ABC \sim \triangle DEF\), corresponding sides are proportional. Let's match the sides: \(BC = 19.5\) corresponds to \(EF = 6\), \(AC = 32.5\) corresponds to \(DF = 10\), and \(AB = x\) corresponds to \(DE = 8\).

Step2: Set Up Proportion

Using the similarity of triangles, \(\frac{AB}{DE}=\frac{BC}{EF}=\frac{AC}{DF}\). Let's use \(\frac{AB}{DE}=\frac{BC}{EF}\), so \(\frac{x}{8}=\frac{19.5}{6}\).

Step3: Solve for \(x\)

Cross - multiply: \(6x = 19.5\times8\). Calculate \(19.5\times8 = 156\). Then \(x=\frac{156}{6}=26\).

Answer:

A. 26