The measures of 2 sides of an equilateral triangle are 4x - 5 and

3x + 1. What is the measure of the third side in centimeters?

clearly, it will be either 4x-5 or 3x+1 cm.

all the sides are the same length

4 x - 5 = 3 x + 1
x = 6
so
3 x +1 = 19
4 x - 5 = 19
and of course the last one is19 :)

LOL but which ?

To find the measure of the third side of the equilateral triangle, we need to remember that in an equilateral triangle, all three sides have equal lengths.

1. Set up an equation using the given measures of the two sides:
4x - 5 = 3x + 1

2. Solve the equation by isolating x:
Subtract 3x from both sides: 4x - 3x - 5 = 3x - 3x + 1
Simplify: x - 5 = 1
Add 5 to both sides: x - 5 + 5 = 1 + 5
Simplify: x = 6

3. Substitute the value of x back into one of the original expressions to find the measure of one side:
Substitute x = 6 into 4x - 5:
4(6) - 5 = 24 - 5 = 19

4. Since all three sides of an equilateral triangle have the same length, the measure of the third side is also 19 centimeters.