Question

Find the length of BC.

Answer 1

BC = 10 units

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.

`(AC)/(BC)=(DC)/(EC)`

`(AB+BC)/(BC)=(DE+EC)/(EC)`

`(2.5+BC)/(BC)=(2+8)/(8)`

`(2.5)/(BC)+1=(10)/(8)`

`(2.5)/(BC)=(5)/(4)-1`

`(2.5)/(BC)=(1)/(4)`

BC = 10