The perimeter of a triangle is 32 feet. one side of the triangle is 11 feet longer than the second side. the third side is 9 feet longer than the second side. find the length of each side.

first side: 15ft

Second side: 4ft

Third side: 13ft

Explanation:

Perimeter is basically the sum of the length of all sides. So since the perimieter is 32 ft, this means that the sum of the length of all sides should be equal to 32 ft.

Let's assign some labels and solve for the

x = first side

y = second side

z = third side

Now let's see what was given:

x + y + z = 32ft

First side is 11 ft longer than the second side

x = y + 11

Third side is 9 ft longer than the second side

z = y + 9

We can use these equations to solve for the rest through substitution:

     x    +     y      +     z     = 32ft

(y + 11) +     y       +   (y + 9)   = 32ft

Let's drop the parentheses:

y + 11 + y + y + 9 = 32ft

Combine like terms:

20 + 3y = 32

Subtract 20 from both sides of the equation:

20 - 20 + 3y = 32 - 20

3y = 12

Divide both sides by 3:

3y/3 = 12/3

y = 4 ft

Now we have the second side.

We then use this in the equations of the other sides:

x = y + 11ft

  = 4ft + 11ft

  = 15ft

z = y + 9ft

 = 4ft + 9ft

 = 13ft

Let's check:

x + y + z = 32ft

15ft + 4ft + 13ft = 32ft

32 ft = 32ft

We're correct!