Question

Find the lengths of DE and EF. Note: Segments BC and DF are parallel.

Answer 1

DE=9

FE=15

Explanation:

Triangle EBC is similar to triangle EDF.

Therefore

`(DE)/(DB)= (FE)/(CE)`

`(5x - 4 + 3)/(3) = (4x + 2 + 5)/(5)`

`(5x - 1)/(3) = (4x + 7)/(5)`

`5(5x - 1) = 3(4x + 7)`

Expand to get;

`25x - 5 = 12x + 21`

Group similar terms:

`25x - 12x = 21 + 5`

`13x = 26`

Divide both sides by 13 to get:

`x = 2`

We substitute to get:

DE= 5x-3+4

DE=5*2-3+4

DE=10-1=9

Also,

FE=4x+2+5

FE =4*2+2+5

FE=8+7

FE=15