The value of x that makes △ABC ~ △XYZ is 0.8.
What are similar triangles?
Two triangles are similar if their corresponding angles are congruent, and the corresponding sides are in proportion. This is known as the Angle-Angle (AA) or Side-Angle-Side (SAS) similarity criteria.
Given that
∆ABC ~ ∆XYZ
The corresponding sides are proportional
AB/XY = BC/YZ = AC/XZ
AB/XY = AC/XZ
5 - x/8.4 = 2.8/5.6
5.6(5 - x) = 8.4 * 2.8
28 - 5.6x = 23.52
5.6x = 28 - 23.52
5.6x = 4.48
x = 4.48/5.6
x = 0.8
The value of x that makes △ABC ~ △XYZ is 0.8.