Answer:
The length of AB is 20 units
Step-by-step explanation:
The equilateral triangle is the triangle that has 3 equal sides and 3 equal angles, the measure of each angle is 60°
∵ All of the angles of triangle ABC measure 60 °
→ By using the fact above
∴ Triangle ABC is an equilateral triangle
→ That means its 3 sides are equal
∴ AB = BC = CA
∵ AB = 3x - 4
∵ BC = 4x - 12
∵ CA = 5x - 20
→ Equate 2 of them to find x
∵ BC = CA
∴ 5x - 20 = 4x - 12
→ Subtract 4x from both sides
∵ 5x - 4x - 20 = 4x - 4x - 12
∴ x - 20 = -12
→ Add 20 to both sides
∴ x - 20 + 20 = -12 + 20
∴ x = 8
→ To find AB substitute the value of x in its expression
∵ AB = 3x - 4
∴ AB = 3(8) - 4
∴ AB = 24 - 4
∴ AB = 20
∴ The length of AB is 20 units
