Question

what value of x will make the triangles similar by the sss similarity theorem? 1.5 20 30 67.5

Explanation:

Step1: Recall SSS Similarity Theorem

For two triangles to be similar by SSS (Side - Side - Side) similarity theorem, the ratios of their corresponding sides must be equal. Let's identify the corresponding sides. The first triangle has sides \(x\), \(x\), and \(50\). The second triangle has sides \(45\), \(45\), and \(75\). So we can set up the proportion \(\frac{x}{45}=\frac{50}{75}\) (matching the equal - length sides and the other side).

Step2: Solve the Proportion for \(x\)

We have the proportion \(\frac{x}{45}=\frac{50}{75}\). Cross - multiply: \(75x = 45\times50\). Calculate \(45\times50 = 2250\). Then, \(x=\frac{2250}{75}\). Divide \(2250\) by \(75\): \(2250\div75 = 30\).

Answer:

30