Question

determining a missing side length
what value of x will make the triangles similar by the sss similarity theorem?
x =
(image of two triangles: first triangle has sides 21, 15, 15; second triangle has sides x, 20, 20)

Explanation:

Step1: Identify SSS similarity ratio

For SSS similarity, the ratios of corresponding sides must be equal. The first triangle has sides 15, 15, 21. The second has sides 20, 20, \( x \). 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:

\( x = 28 \)