#### Answer

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.