Answer:
[tex]\overline{ \sf AC} = 14 \textsf{units}[/tex]
Step-by-step explanation:
To find the length of side [tex]\overline{ \sf AC}[/tex], let's use the given information about the perimeter:
The perimeter of a triangle is the sum of the lengths of its three sides.
So, we have
[tex] \sf \overline{\sf AB} +\overline{\sf BC} + \overline{\sf AC} = 41 [/tex]
Substitute the value of AB, BC, and AC:
[tex] (3z - 2) + (z + 1) + (2z) = 41 [/tex]
Combine like terms:
[tex] (3z+z+2z) -2+1 =41 [/tex]
[tex] 6z - 1 = 41 [/tex]
Now, solve for z:
[tex] 6z = 41+1 [/tex]
[tex] 6z = 42 [/tex]
[tex] z =\dfrac{42}{6}[/tex]
[tex] z = 7 [/tex]
Now that we the value of z, we can find the length of side [tex]\overline{ \sf AC}[/tex],
[tex] \overline{\sf AC }= 2z = 2(7) = 14 [/tex]
So, the length of side [tex]\overline{ \sf AC}[/tex] is 14 units.
