ANSWER
• W = 10
,
• L = 16
Step-by-step explanation
Let W be the width of the rectangle and L the length. We know that "the length is 4 less than twice the width" which translates as:

The perimeter, which is 52, is twice the length plus twice the width:

We have two equations with two variables. We can use the substitution method to solve the system. Replace the first equation of L as a function of W in the second equation:

And solve for W. First we have to apply the distributive property to the parenthesis expression:

Then we add like terms:

Add 8 on both sides of the equation:

And divide both sides by 6:

Now we have that W = 10. Replace this value in the first equation we had to find L:

So L = 16