The sum of length and width is half the perimeter, so is (70 in)/2 = 35 in. Since this is the sum of length and width, if we add 5 inches, it will be twice the length. That is ...
... length + width = 35 in
... length + (width + 5 in) = (35 in) + (5 in)
... 2×length = (35 in) + (5 in) = 40 in
The length of the rectangle is 20 inches.