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,

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

So, the value of x = 7

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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,

$\frac{AB}{AC}=\frac{BD}{CE}$

AB = 4

AC = 4+6 = 10

CE = 30

So,

$\begin{gathered} \frac{4}{10}=\frac{BD}{30} \\ 10\cdot BD=4\cdot30 \\ 10\cdot BD=120 \\ \\ BD=\frac{120}{10}=12 \end{gathered}$

So, the length of BD = 12