Can someone give deeply explain this?

Step-by-step explanation (solution):

We are told that the length is "8 cm more than three times its width":

We are told that the perimeter is 128 cm. Use the formula for the perimeter of a rectangle:

Insert known values:

Simplify to find the value of w. Use the distributive property:

Combine like terms by addition:

Subtract 16 from both sides (inverse operations):

Isolate the variable. Divide both sides by 8 (inverse operations):

The width is 14 cm. Insert this value into the original equation for perimeter and solve for the length:

Subtract 28 from both sides (inverse operations):

Divide both sides by 2 (inverse operations):

The length is 50 cm.

Check values:

Insert the value of the length and width for "8 cm more than three times its width":

The given values are true.

:Done