Question

which proportion could be used to find the missing side length, x? a. \\(\frac{x}{64} = \frac{36}{36}\\) b. \\(\frac{x}{64} = \frac{72}{36}\\) c. \\(\frac{x}{64} = \frac{36}{72}\\) d. none of the above. there is not enough information to solve for the missing side length.

Explanation:

Step1: Identify Similar Triangles

The two triangles are similar (same angle \(57^\circ\), and the line is parallel, so AA similarity). Corresponding sides are proportional. The large triangle has sides \(64\) (corresponding to \(x\)) and \(36 + 36 = 72\) (corresponding to \(36\)).

Step2: Set Up Proportion

For similar triangles, \(\frac{\text{side of large triangle}}{\text{side of small triangle}}=\frac{\text{other side of large triangle}}{\text{other side of small triangle}}\). So \(\frac{x}{64}=\frac{36}{72}\) (or simplified, but this matches option C).

Answer:

C. \(\frac{x}{64}=\frac{36}{72}\)