the first side of a triangle measures 3 cm longer then the second side the third side is 4cm shorter then twice the second side the perimeter is 31cm. how long is each side?

second side = s

s+3
s
2s-4

s+3+s + 2s - 4 = 31
4 s = 32
s = 8
so
11
8
12

858648648

To find the lengths of the sides of the triangle, let's assign variables to the sides:

Let the second side of the triangle be x cm.
The first side will then be x + 3 cm.
The third side will be 2x - 4 cm, as it is 4 cm shorter than twice the second side.

According to the question, the perimeter of the triangle is 31 cm. We can use this information to set up an equation:

Perimeter = Sum of all three sides

31 cm = x + (x + 3) + (2x - 4)

Now, let's solve the equation to find the value of x:

31 cm = 4x - 1

Adding 1 to both sides of the equation:

32 cm = 4x

Dividing both sides by 4:

8 cm = x

Now that we know the value of x, we can substitute it back into our earlier equations to find the lengths of all three sides:

First side = x + 3 = 8 + 3 = 11 cm
Second side = x = 8 cm
Third side = 2x - 4 = 2(8) - 4 = 12 cm

So, the lengths of the sides of the triangle are:
First side: 11 cm
Second side: 8 cm
Third side: 12 cm