Question

the perimeter of the triangle below is 47 units. find the value of z.
$3z$
$2z + 2$
$z + 3$
$z = \square$

Explanation:

Step1: Sum all side lengths

$3z + (2z + 2) + (z + 3)$

Step2: Simplify the expression

$3z + 2z + 2 + z + 3 = 6z + 5$

Step3: Set equal to perimeter

$6z + 5 = 47$

Step4: Solve for z (subtract 5)

$6z = 47 - 5 = 42$

Step5: Isolate z (divide by 6)

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

Answer:

$z = 7$