Triangle DEF is similar to triangle GHK. What is the value of DF if GK is 3.4 inches, EF is 2.25 inches, and HK is 9 inches?

Triangles are similar if their corresponding (matching) angles are congruent (equal in measure) and the ratio of their corresponding sides are in proportion. So the length of of DF can be solve by ratio and proportion

(EF / HK) = (DF / GK)

(2.25 / 9) = DF / 3.4

DF = (2.25 / 9) * 3.4

DF = 0.85