The length BC in the figure is 8.
How the length of line BC is calculated.
Similar triangles are polygons with corresponding angles that are equal and corresponding sides that are in proportion. They have the same shape but may differ in size.
Given that
AB = 10, BD = 5 and DE = 12
BC is parallel to DC
∠A is congruent to ∠A( reflective property of congruence)
∆ABC is similar to ∆ADE
For similar triangles the corresponding sides are proportional.
Therefore,
BC/DE = AB/AD
AD = AB + BD
= 10 + 5
= 15
Substitute into BC/DE = AB/AD
BC/12 = 10/15
15BC = 12*10
15BC = 120
BC = 120/15
BC = 8
Therefore, the length BC in the figure is 8.