# SOLUTION: 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 triang

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 Geometry: Triangles Solvers Lessons Answers archive Quiz In Depth

 Question 206886: 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!Found 2 solutions by jim_thompson5910, Edwin McCravy:Answer by jim_thompson5910(28598)   (Show Source): You can put this solution on YOUR website!If ABC is similar to DEF, then the corresponding sides form a ratio. In other words, the ratio of AB to DE is the same as the ratio of BC to EF. Similarly, the ratio of BC to EF is equal to the ratio of AC to DF. What this means is and if you plug in the given lengths, you get (which is indeed true). Furthermore, this means that and plugging in the given values gets us . So all you need to do from here is solve for 'n' Note: because all the ratios are equal, we can also solve the equation and get the same answer. Answer by Edwin McCravy(8909)   (Show Source): You can put this solution on YOUR website!Edwin's solution: 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! ``` 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: Substitute their lengths: Reducing the fractions: Cross multiply: Edwin```