Answer:
BC = 10 units
Step-by-step explanation:
From the picture attached,
It's given that AD and BE are the parallel sides.
AC and DC are the transversal lines intersecting the parallel lines.
In ΔADC and ΔBEC,
∠DAC ≅ ∠EBC [Corresponding angles]
∠ADC ≅ ∠BEC [Corresponding angles]
ΔADC ~ ΔBEC [By AA property of similar triangles]
By the property of similar triangles,
Corresponding sides of the similar triangles are proportional.
[tex]\frac{AC}{BC}=\frac{DC}{EC}[/tex]
[tex]\frac{AB+BC}{BC}=\frac{DE+EC}{EC}[/tex]
[tex]\frac{2.5+BC}{BC}=\frac{2+8}{8}[/tex]
[tex]\frac{2.5}{BC}+1=\frac{10}{8}[/tex]
[tex]\frac{2.5}{BC}=\frac{5}{4}-1[/tex]
[tex]\frac{2.5}{BC}=\frac{1}{4}[/tex]
BC = 10
