Question

what value of x will make the triangles similar by the sss similarity theorem? x =
(first triangle: sides 21, 15, 15; second triangle: sides x, 20, 20)

Explanation:

Step1: Identify corresponding sides

The first triangle has sides 15, 15, 21. The second has sides 20, 20, \( x \). For SSS similarity, ratios of corresponding sides must be equal. So, \(\frac{15}{20}=\frac{21}{x}\) (matching the equal - length sides and the remaining sides).

Step2: Solve the proportion

Cross - multiply: \(15x = 21\times20\). Calculate \(21\times20 = 420\). Then, \(x=\frac{420}{15}\). Simplify \(\frac{420}{15}=28\).

Answer:

28