All of the angles of Triangle ABC measure 60 o. AB = 3x – 4, BC = 4x – 12 and CA = 5x – 20. Solve for x and find the length of AB.

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

c. (3,2,6) is the answer.