Question

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

Explanation:

Step1: Identify corresponding sides

The first triangle has sides 50, x, x; the second has 75, 45, 45. Corresponding sides: 50↔75, x↔45, x↔45.

Step2: Set up similarity ratio

Ratio of first to second triangle: $\frac{50}{75} = \frac{2}{3}$.

Step3: Solve for x

$\frac{x}{45} = \frac{2}{3} \implies x = 45 \times \frac{2}{3} = 30$.

Answer:

30