Answer:
The length of DE is 11
Explanation:
Let us solve the question
∵ B is the midpoint of AC
∴ AB = BC
∵ AB = 3x + 4
∴ BC = 3x + 4
∵ AC = AB + BC
→ Substitute the expressions of AB and BC
∴ AC = 3x + 4 + 3x + 4
→ Add the like terms
∵ AC = (3x + 3x) + (4 + 4)
∴ AC = 6x + 8
∵ AC = 11x - 17
→ Equate the right sides of the AC
∴ 11x - 17 = 6x + 8
→ Subtract 6x from both sides
∵ 11x - 6x - 17 = 6x - 6x + 8
∴ 5x - 17 = 8
→ Add 17 to both sides
∵ 5x - 17 + 17 = 8 + 17
∴ 5x = 25
→ Divide both sides by 5
∴ x = 5
→ Substitute the value of x in AC to find its length
∵ AC = 11(5) -17 = 55 - 17
∴ AC = 38
∵ AC = CD
∴ CD = 38
∵ CE = 49
∵ CE = CD + DE
→ Substitute the lengths of CE and CD
∴ 49 = 38 + DE
→ Subtract 38 from both sides
∵ 49 - 38 = 38 - 38 + DE
∴ 11 = DE
∴ The length of DE is 11