Question

Given the diagram below with line DE║ line AC. Find BC.

Answer 1

13.5

Explanation:

In triangle ABC, DE || AC

Therefore by basic proportionality theorem:

`(BD)/(DA) = \frac {BE}{EC} \\\\</p><p>\therefore (4)/(8) = \frac {BE}{9} \\\\</p><p>\therefore (1)/(2) = \frac {BE}{9} \\\\</p><p>\therefore BE = (9)/(2) \\\\</p><p>\therefore BE = 4.5\\</p><p>\because BC = BE + EC \\</p><p>\therefore BC = 4.5 + 9\\</p><p>\huge \red {\boxed {\therefore BC = 13.5}} \\`