Question

what value of x will make the triangles similar by the sss similarity theorem? x = 15 21 15 x 20 20

Explanation:

Step1: Identify corresponding sides

First triangle sides: 15, 15, 21; second triangle sides: 20, 20, x. Corresponding sides: 15↔20, 15↔20, 21↔x.

Step2: Set up proportion for similarity

For SSS similarity, ratios of corresponding sides are equal: $\frac{15}{20} = \frac{21}{x}$

Step3: Solve for x

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

Answer:

28