Answer:
Labelled the diagram as shown below
Given triangle ABC and triangle CDE are similar.
by definition of similar triangle:
Corresponding sides are in proportion:
[tex]\frac{AC}{DC} =\frac{BC}{CE}[/tex]
Here, AC = 8 units, DC =8+6 = 14 units, and BC = 2x-2 units and CE= 3x units.
Substitute these we have;
[tex]\frac{8}{14} =\frac{2x-2}{3x}[/tex]
Simplify:
[tex]\frac{4}{7} =\frac{2x-2}{3x}[/tex]
By cross multiply we have;
[tex]12x = 7(2x-2)[/tex]
Using distributive property: [tex]a\cdot (b+c) = a\cdot b+ a\cdot c[/tex]
[tex]12x = 14x-14[/tex]
Subtract 14x from both sides we get;
[tex]-2x = -14[/tex]
Divide by b-2 to both sides we get;
x = 7
Therefore, the value of x is, 7
