Answer
The shortest side equals 8 cm.
The longest side is 17 cm.
The other side is 15 cm.
Work Step by Step
Let X represent the shortest side.
The longest side is 1 centimeter longer than twice the shortest side, which equals 1 + 2X.
The other side is 2 centimeters shorter than the longest side. It equals 1 + 2X - 2 = 2X - 1.
The perimeter of a triangle is equal to the sum of all its sides.
The perimeter of a triangle is 40 centimeters, so we can set up the following equation:
X + 1 + 2X + 2X - 1 = 40
5X = 40
Divide both sides by 5.
X = 8
The shortest side equals 8.
The longest side is 1 + 2 $\times$ 8 = 1 + 16 = 17.
The other side is 2 $\times$ 8- 1 = 15.
