Question 1111585
Let "x" represent the length of side 1; let "y" represent the length of side 2; and let "z" represent the length of side 3.  Since the entire perimeter of the triangle is 50 cm, we know that:

    x + y + z = 50

Since the length of side 1 ("x") is three less than 4 times the length of side 2 ("y"), we have:

    x = 4y - 3

Since the length of side 3 ("z") is 5 cm longer than the length of side 2 ("y"), we have:

    z = y + 5

So we now have three simultaneous equations with three variables:

     x + y + z = 50
     x         = 4y - 3
             z = y + 5

Using substitutions from the last two equations into the first, we have:

    (4y - 3) + y + (y + 5) = 50

Gathering like terms, we have:

          6y + 2 = 50

Subtracting 2 from both sides, we have:

          6y = 48

Dividing both sides by 6, we have:

           y = 8

So, we know the length of side 2 ("y") is 8.

Substituting 8 in for y in the other two equations, we have:

         x = (4 * 8) - 3
         x =  32 - 3
         x = 29     so the length of side 1 ("x") is 29

         z = 8 + 5
         z = 13     so the length of side 3 ("z") is 13

Let's add them all together to make sure that the perimeter is 50:
        
         29 + 8 + 13 = 50   yep, it checks