Question

Given: △ABC,

ADEF rhombus
D∈AB, E∈BC, F∈AC
AB=14, BC=12, AC=10
Find: BE and EC

Answer 1

BE=7 un., EC=5 un.

Explanation:

Triangles ABC and ADE are similar, then

`(14)/(14-x)=(12)/(BE)=(10)/(x).`

Thus,

`14x=10(14-x),\\ \\14x=140-10x,\\ \\24x=140,\\ \\x=(140)/(24)=(35)/(6)\ un..`

Therefore,

`(12)/(BE)=(10)/((35)/(6)),\\ \\10BE=12\cdot (35)/(6),\\ \\10BE=70,\\ \\BE=7\ un.`

So
`EC=BC-BE=12-7=5\ un.`