Answer:
40 units
Step-by-step explanation:
Given:
Perimeter of ∆ABC = 85 units
AC = 4z
AB = 3z + 3
BC = z + 2
Required:
Numerical value of AC
SOLUTION:
Perimeter of ∆ = sum of all its sides
Perimeter of ∆ABC = AC + AB + BC
85 = 4z + (3z + 3) + (z + 2)
Use this equation to find the value of the variable, z
[tex] 85 = 4z + 3z + 3 + z + 2 [/tex]
Collect like terms
[tex] 85 = 8z + 5 [/tex]
Subtract 5 from both sides
[tex] 85 - 5 = 8z [/tex]
[tex] 80 = 8z [/tex]
Divide both sides by 8
[tex] 10 = z [/tex]
[tex] z = 10 [/tex]
AC = 4z
Plug in the value of x
AC = 4(10)
AC = 40 units
