Answer
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.
