The first side is 6 cm. The second side is 19 cm. The third side is 21 cm.
Work Step by Step
Let X represent the first side. The second side is 1 centimeter longer than three times the first side, which equals 3X + 1. The third side is 2 centimeters longer than the second side. Since the second side is 3X + 1, the third side equals 3X + 1 + 2 = 3X + 3. The perimeter of a triangle is equal to the sum of all its sides. Since the perimeter of the triangle is 46, we can set up the following equation: X + 3X + 1 + 3X + 3 = 46 7X + 4 = 46 Subtract 4 from both sides. 7X = 42 Divide both sides by 7. X = 6 The first side is 6. The second side is 3 $\times$ 6 + 1 = 19. The third side is 3 $\times$ 6 + 3 = 21.