Question

32 multiple choice 1 point the triangles are similar. what is the value of x. 6 20 8/3 24

Explanation:

Step1: Determine corresponding sides

Since the triangles are similar, the ratio of corresponding sides is equal. The side of length \(8\) in the first triangle corresponds to side \(x\) in the second triangle, and the side of length \(12\) in the first triangle corresponds to side \(y\), and the side of length \(4\) in the second triangle corresponds to side \(8\) in the first triangle (by angle - side correspondence as the angles are \(60^{\circ},100^{\circ}\)). The ratio of similarity is \(\frac{4}{8}=\frac{1}{2}\) (smaller triangle to larger triangle). Or using the proportion \(\frac{\text{side in smaller triangle}}{\text{side in larger triangle}}\). If we consider the sides \(4\) (smaller triangle) and \(8\) (larger triangle), and for the other pair of corresponding sides \(x\) (smaller triangle) and \(12\) (larger triangle).

Step2: Set up proportion

Using the property of similar triangles \(\frac{x}{12}=\frac{4}{8}\). Cross - multiply gives \(8x = 12\times4\).

Step3: Solve for \(x\)

First, calculate \(12\times4 = 48\). Then \(8x=48\), so \(x=\frac{48}{8}=6\).

Answer:

A. 6