One side of a triangular banner is 1 ½ times longer than the second side and 2 cm shorter than the third side. The perimeter of the triangle is 98 cm. How long is the shortest side?

x + x/(3/2) + x+2 = 98

x = 36

so, the sides are 36,24,38

To solve this problem, let's assign variables to the sides of the triangle. Let's call the second side "x" cm.

According to the problem, the first side is 1 ½ times longer than the second side. Therefore, the first side can be represented as 1.5x cm.

The third side is 2 cm shorter than the first side, so it can be represented as (1.5x - 2) cm.

Now, we know that the perimeter of the triangle is 98 cm, which means the sum of all three sides is 98 cm.

So we can write the equation: x + 1.5x + (1.5x - 2) = 98

Simplifying the equation, we get:
4x + (1.5x - 2) = 98
4x + 1.5x - 2 = 98
5.5x - 2 = 98
5.5x = 100
x = 100 / 5.5
x ≈ 18.18

The shortest side of the triangle is x, which is approximately 18.18 cm.