The perimeter of a triangle is 72 cenimeters.the second side is twice as long as the first side.the third side is four centimeters shorter than the second side.how long is the first side?

Let the first side length be A, etc.

A + B + C = 72
B = 2A
C = B-4

B/2 + B + (B -4) = 2.5 B -4 = 72
2.5 B = 76
B = 30.4
A = 15.2 is the first side length
C = 26.4
--------
Sum = 72, as required

To find the length of the first side of the triangle, we can set up an equation using the given information.

Let's assume the first side is represented by "x" centimeters.

According to the given information, the second side is twice as long as the first side, so the second side would be 2x centimeters.

The third side is four centimeters shorter than the second side, so the third side would be (2x - 4) centimeters.

Now, we can use the formula for the perimeter of a triangle, which is the sum of all three sides.

Perimeter = First Side + Second Side + Third Side

72 = x + 2x + (2x - 4)

Simplifying the equation:

72 = 5x - 4

Adding 4 to both sides:

76 = 5x

Dividing both sides by 5:

x = 76/5

So, the length of the first side of the triangle is 15.2 centimeters.