Answer:
n = 16, AC = 60, DE = 30
Step-by-step explanation:
DE joins the midpoints of 2 sides of the triangle and is half the length of the third side, that is
DE = [tex]\frac{1}{2}[/tex] AC , substitute values
n + 14 = [tex]\frac{1}{2}[/tex] (3n + 12) ← multiply both sides by 2 to clear the fraction
2n + 28 = 3n + 12 ( subtract 2n from both sides )
28 = n + 12 ( subtract 12 from both sides )
16 = n
Then
AC = 3n + 12 = 3(16) + 12 = 48 + 12 = 60
DE = n + 14 = 16 + 14 = 30
