Question

I would like some help with a two part question. Please and thank you.

Answer 1

Given the triangle ACE

BD // CE

So, the segments between the parallel lines will be proportional

AB = 4

BC = 6

AD = x+3

DE = 2x+1

so,

`\begin{gathered} (AB)/(BC)=(AD)/(DE) \\ \\ (4)/(6)=(x+3)/(2x+1) \\ \\ 4\cdot(2x+1)=6\cdot(x+3) \\ 8x+4=6x+18 \\ 8x-6x=18-4 \\ 2x=14 \\ \\ x=(14)/(2)=7 \end{gathered}`

So, the value of x = 7

============================================================

Given if CE = 30

We need to find the length of BD

So, using the similarity between the triangles ABD and ACE

So, the corresponding sides will be proportionals

So,

`(AB)/(AC)=(BD)/(CE)`

AB = 4

AC = 4+6 = 10

CE = 30

So,

`\begin{gathered} (4)/(10)=(BD)/(30) \\ 10\cdot BD=4\cdot30 \\ 10\cdot BD=120 \\ \\ BD=(120)/(10)=12 \end{gathered}`

So, the length of BD = 12