I'll use W for the width and L for the length, both in feet.
We are told that the length is twice the width, plus 1: L = 2W + 1
We know that L*W = Area, which is 15 ft2 so: L*W = 15 ft2
Use the equation for length in the second equation:
L*W = 15 ft2
(2W + 1)*W = 15 ft2
2W2 + W - 15 = 0
(W + 3)*(2W - 5) = 0
Therefore, there are two possible answers:
W = -3, and
W = (5/2)
We can't have a negative length, unless we are in a Star Wars movie. The answer is the remaining solution: W = 2.5 ft
Length is found from the first equation: L = 2W + 1
L = 2(5/2) + 1
L = 6 ft
Multiply the two values for L and W to see if we get 15 ft2.
(5/2 ft)*(6 ft) = 15 ft2
The answers work. L = 6 ft and W = 2.5 ft.