Raymond B. answered • 06/03/19

Math, microeconomics or criminal justice

The other 3 answers are all correct. But there's a danger lurking in this type of question. Let's say the problem were slightly different, with perimeter = 38, C=A+8 and A=2B. Work it mechanically the same way substituting from 38=A+B+C to get 38=2B+B+2B+8=5B+8 and solve for B, B=6, A=2B=12 C=12+8=20. Check the math, it's all correct. Then the surprise, There is no such triangle with sides 6, 12 and 20. No such triangle exists. The given problem perimeter=35 with solution 6, 12, 17 involves a very flat or obtuse triangle. A little perspective sometimes helps. For the given problem with perimeter = 35, the longest side of a triangle would have to be somewhere between 1/3 and 1/2 of that perimeter, or between about 12 and 17. If the longest side were 17.5, it's no longer a triangle, just a flat line or a "triangle" with angles 0, 0 and 180 degrees. IF you encountered a problem like this that had no solution, maybe that's n unfair trick question. But some instructors will do it to you, sometimes accidentally, as they just make up some numbers that seem to lead to a solution, but where no real triangle can exist with those 3 sides.