Question 521629
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