The width of a rectangle is two-thirds the length, the perimeter of the rectangle is 15. What is the length?

W = 2/3l

15 = 2l + 2w

Because we have a value for w, we'll place it in the second equation.

15 = 2l + 2 (2/3l)

15 = 2l + 4/3l

Multiply all terms by 3.

45 = 6l + 4l

Combine.

45 = 10l

Divide both sides by 10.

4.5 = l

The value of the length is 4.5.