SOLUTION: Suppose ABC~JKL with BC=28, JK=12, and KL=42. Find the perimeter of ABC if the perimeter of JKL is 72 A. 60 B. 48 C. 18 D. 12 Thank you so much, I am completely clueless o

Algebra ->  Angles -> SOLUTION: Suppose ABC~JKL with BC=28, JK=12, and KL=42. Find the perimeter of ABC if the perimeter of JKL is 72 A. 60 B. 48 C. 18 D. 12 Thank you so much, I am completely clueless o      Log On


   

Question 286895: Suppose ABC~JKL with BC=28, JK=12, and KL=42. Find the perimeter of ABC if the perimeter of JKL is 72
A. 60
B. 48
C. 18
D. 12
Thank you so much, I am completely clueless on how to work this
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Since the perimeter of JKL is 72, and we know two sides of JKL, we can easily solve for the missing length JL by remembering that

Perimeter = side1+side2+side3

So 72=12%2B42%2BJL. Solve for JL to get JL=18


Since ABC~JKL (triangle ABC is similar to triangle JKL), we can set up the ratios:

AB%2FJK=BC%2FKL and AC%2FJL=BC%2FKL


note: it might help to draw out the triangles to see what's going on.


AB%2FJK=BC%2FKL Start with the first equation


AB%2F12=28%2F42 Plug in BC=28, JK=12, and KL=42


AB%2F12=2%2F3 Reduce.


AB=%282%2F3%29%2A12 Multiply both sides by 12


AB=24%2F3 Multiply


AB=8 Reduce.


So one side of ABC is AB = 8



AC%2FJL=BC%2FKL Move onto the second equation


AC%2F18=28%2F42 Plug in BC=28, JL=18, and KL=42


AC%2F18=2%2F3 Reduce.


AC=%282%2F3%29%2A18 Multiply both sides by 18


AC=36%2F3 Multiply


AC=12 Reduce.


So the last side of ABC is AC = 12


Now just add up the sides AB = 8, BC = 28, and AC = 12 to get the perimeter of ABC:

P = 8+28+12 = 48


So the perimeter of ABC is 48 units.


Note: the ratio of the perimeter of ABC to the perimeter of JKL is the same as the ratio of any two corresponding sides. This saves us a lot of work, but it's always good to take the long way so we can see what's going on.