Triangle ABC is similar to Triangle DEF. AB=2x+4, AC=4x+1, ED=6x squared+14x+4, EF=9x squared+9x+2, DF=12x squared+7x+1. What is BC? Drawing below...

Question

anonymous · Answer

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yttrium · Answer

Do you know that the corresponding sides of similar triangles are proportional?

anonymous · Answer

yeah..

anonymous · Answer

@Yttrium

yttrium · Answer

Then, you can formulate a formula for BC using ratio and proportion. Can you?

anonymous · Answer

AB/DE = AC/DF

anonymous · Answer

@Yttrium

yttrium · Answer

Use the segment BC because that is what we are going to solve.

anonymous · Answer

oh yeah, sorry... BC/EF=AC/DF @Yttrium

yttrium · Answer

Can you plug in the values?

yttrium · Answer

@ksalimios

anonymous · Answer

$$BC/9X ^{2} = 4X+1/12X ^{2}+7X$$

yttrium · Answer

Then BC will be equal to what?

anonymous · Answer

i don't know

yttrium · Answer

You know cross-multiplication?

anonymous · Answer

yeah.. so $$\left( BC \right)\left( 12X ^{2} +7X+1\right)= \left( 4X+1 \right)\left( 9X ^{2}+9X+2 \right)$$

yttrium · Answer

Yes, but bring down the term beside BC and factor it out

anonymous · Answer

that's my problem.. the factoring part

anonymous · Answer

@Yttrium

yttrium · Answer

Well, this kind of lesson for me is hard to teach. But if you know the foil method of multiplication, it's better. I can teach you quicker.

anonymous · Answer

can you teach me please?? @Yttrium

yttrium · Answer

Awww. I need to log out now. :((
Just ping me if you see me online here so I can still teach you about this topic. But anyway, this is your 1st incentive from me. :)
$$BC = \frac{ (4x+1)(3x+1)(3x+2) }{ (3x+1)(4x+1) }$$

anonymous · Answer

thank u @Yttrium .. it means a lot..