The greatest length the first side can be is 15 cm and the greatest length the second side can be is 45 cm.
Work Step by Step
Let x represent one side of the triangle. The other side is 3 $\times$ x = 3x. The perimeter = x + 3x + 15 The perimeter = 4x + 15 Because the perimeter of the triangle is to be no greater than 75 centimeters, we set up the following inequality. 4x + 15 $\leq$ 75 4x $\leq$ 60 Divide both sides by 4. x $\leq$ 15 The maximum value x, or the first side, can be is 15 cm. The maximum value the second side can be is 15 $\times$ 3 = 45 cm.