one side of the triangular banner is 1 1/2 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 shorter side?

One side is x

The next side is 2/3 x
The last side is x+2

x + 2x/3 + x+2 = 98
Find x, then the short side is 2/3 x.

To solve this problem, we can set up an equation based on the given information.

Let's assume the shorter side of the triangular banner is represented by "x" cm.

According to the problem, we know that the first side of the banner is 1 1/2 times longer than the second side, so we can represent the first side as (3/2)x cm.

Additionally, the first side is 2 cm shorter than the third side, so we can represent the third side as [(3/2)x + 2] cm.

Now, we can use the formula for the perimeter of a triangle to set up an equation:

Perimeter = first side + second side + third side

98 cm = (3/2)x cm + x cm + [(3/2)x + 2] cm

To solve this equation, we can first simplify it:

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

Next, we can combine like terms:

98 cm = (4x/2) cm + (3/2)x cm + 2 cm

98 cm = (7/2)x cm + 2 cm

To eliminate the 2 cm on the right side of the equation, we can subtract 2 cm from both sides:

98 cm - 2 cm = (7/2)x cm

96 cm = (7/2)x cm

To isolate x, we can multiply both sides by 2/7:

96 cm * (2/7) = x cm

Now, we can calculate x:

x ≈ 27.43 cm

Therefore, the shorter side of the triangular banner is approximately 27.43 cm long.