In the figure below, what is the measure of AB?

The measure of AB is 29

Step-by-step 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

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