Question 521629: in triangle ABC, line AB is 9 cm shorter than line AC, while line BC is 3 cm longer than line AC. If the perimeter of the triangle is 48 cm, find the lenghts of the 3 sides.
Answer by jlshires(17)   (Show Source):
You can put this solution on YOUR website! Since all the sides are being compared to AC, AC is your x.
Let AC = x
Let AB = 9 cm shorter than AC = x-9
Let BC = 3 cm longer than AC = x+3
The perimeter of a triangle is all of the sides added, therefore AC + AB + BC
the perimeter is 48
AC + AB + BC = 48 substitute in your formulas for the sides
x + (x-9) + (x+3) = 48
factor out the addition signs to get rid of the parentheses
x+x-9+x+3=48
combine like symbols
3x - 6 = 48
add 6 to both sides
3x = 54
divide both sides by 3
x = 18
Put 18 back into your original formulas to find out the lengths of all three sides:
Let AC = x = 18
Let AB = 9 cm shorter than AC = x-9 = 18-9 = 9
Let BC = 3 cm longer than AC = x+3 = 18+3 = 21
the sides are 18, 9, and 21
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