Question

determining a missing side length
what value of x will make the triangles similar by the
sss similarity theorem?
x =

Explanation:

Step1: Identify corresponding sides

The first triangle has sides 15, 15, 21; the second has sides 20, 20, \(x\). Corresponding sides: 15↔20, 21↔\(x\).

Step2: Set up proportion

Since SSS similarity requires equal ratios: \(\frac{15}{20} = \frac{21}{x}\)

Step3: Solve for \(x\)

Cross-multiply: \(15x = 21×20\) → \(15x = 420\) → \(x = \frac{420}{15} = 28\)

Answer:

28