Question 206886
<font size = 8 color = "red"><b>Edwin's solution:</b></font>
I'm having trouble understanding this statement: If triangle ABC is similar to triangle DEF
AB=4, BC=8, AC=11
DE=10, EF=20, DF=n  Solve for n.

I know the perimeter of a triangle is P=a+b+c but I can't seem to solve for n. It's like there are 2 unknowns. Can you please let me know what I am doing wrong. Thank-you!

<pre><font size = 4 color = "indigo"><b>

{{{drawing(400,223.529,-2,32,-2,17, 

triangle(0,0,4,0,9.125,6.142831188), triangle(8,0,18,0,30.8125,15.35707797),

locate(0,0,A), locate(4,0,B), locate(9.2,6.2,C), locate(8,0,D),
locate(18,0,E), locate(31,16,F), locate(25,8,20), locate(17,8,n),
locate(13,0,10), locate(2,0,4), locate(6.5,3,8), locate(2,4,11)

)}}}

You're supposed to do this by proportions:

      (DF is to AC) as (DE is to AB) as (EF is to BC)

Write the proportion as an equation:

            {{{DF/AC = DE/AB = EF/BC}}}

Substitute their lengths:

            {{{n/11 = 10/4 = 20/8}}}

Reducing the fractions:

            {{{n/11 = 5/2 = 5/2}}}

            {{{n/11 = 5/2}}}

Cross multiply:

            {{{2n=55}}}

            {{{n=55/2=27&1/2}}}

Edwin</pre>