Question

In triangle ABC , points D and E are on sides AB and BC , respectively, such that DE is parallel to AC and AD : DB = 3:5. If DB = 6.3 and AC = 9.4 , what is the length of DE ,to the nearest tenth

Answer 1

Answer:

In triangle ABC,

DE||BC

triangle ADE is similar to triangle ABC

Therefore, AD/AB = DE/BC

5/9 = DE/BC -Equation 1

In triangle DEF and BFC

angle EDF = angle BCF (alternate angles)

angle DFE = angle CFB (vertically opposite angles)

so, triangle DEF is similar to triangle BFC

Therefore, arDEF/arBFC

DE square/BC square = 5*5/9*9

=25/81