Answer:
AB is 104
Step-by-step explanation:
In the given figure
∵ CE bisects the segment AB
→ That means CE intersects AB at the midpoint of AB
∵ CE ∩ AB at point F
∴ F is the midpoint of AB
→ The midpoint of a segment divides it into two equal parts
∵ The point F divides AB to FA and FB
∴ FA = FB
∵ FA = 7x + 10
∵ FB = 9x - 2
→ Equate them
∴ 9x - 2 = 7x + 10
→ Add 2 to both sides
∵ 9x - 2 + 2 = 7x + 10 + 2
∴ 9x = 7x + 12
→ Subtract 7x from both sides
∵ 9x - 7x = 7x - 7x + 12
∴ 2x = 12
→ Divide both sides by 2
∴ x = 6
→ Substitute the value of x in FA and FB
∵ FA = 7(6) + 10 = 42 + 10 = 52
∵ FB = 9(6) - 2 = 54 - 2 = 52
∵ AB = FA + FB
∴ AB = 52 + 52 = 104
∴ AB = 104
