Question

The perimeter of the triangle below is 41 units. Find the length of side AC.
Write your answer without variables.

Answer 1

Answer:

$\overline{ \sf AC} = 14 \textsf{units}$

Step-by-step explanation:

To find the length of side $\overline{ \sf AC}$, 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

$\sf \overline{\sf AB} +\overline{\sf BC} + \overline{\sf AC} = 41$

Substitute the value of AB, BC, and AC:

$(3z - 2) + (z + 1) + (2z) = 41$

Combine like terms:

$(3z+z+2z) -2+1 =41$

$6z - 1 = 41$

Now, solve for z:

$6z = 41+1$

$6z = 42$

$z =\dfrac{42}{6}$

$z = 7$

Now that we the value of z, we can find the length of side $\overline{ \sf AC}$,

$\overline{\sf AC }= 2z = 2(7) = 14$

So, the length of side $\overline{ \sf AC}$ is 14 units.