Question

Determine the length of AC and DE, and the value of x.

Answer 1

n = 16, AC = 60, DE = 30

Explanation:

DE joins the midpoints of 2 sides of the triangle and is half the length of the third side, that is

DE =
`(1)/(2)` AC , substitute values

n + 14 =
`(1)/(2)` (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