Answer:
The measure of AB is 29
Explanation:
If a line is drawn from a vertex of a triangle perpendicular to the opposite side to this vertex and bisects it, then the sides joining this vertex are equal in lengths
In Δ ABD
∵ Line AC ⊥ side BD
∵ BC = BD = 15
∴ C is the mid-point of The side BD
∴ Line AC is a perpendicular bisector of side BD
→ By using the rule above
∴ AB = AD
∵ AB = 5x - 11
∵ AD = 3x + 5
→ Equate them
∴ 5x - 11 = 3x + 5
→ Add 11 to both sides
∵ 5x - 11 + 11 = 3x + 5 + 11
∴ 5x = 3x + 16
→ Subtract 3x from both sides
∵ 5x - 3x = 3x - 3x + 16
∴ 2x = 16
→ Divide both sides by 2
∴ x = 8
→ Substitute the value x in the expression of side AB
∵ AB = 5(8) - 11
∴ AB = 40 - 11
∴ AB = 29
∴ The measure of AB is 29