Hello, Reggion,

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 ft^{2} so: L*W = 15 ft^{2}

Use the equation for length in the second equation:

L*W = 15 ft^{2}

(2W + 1)*W = 15 ft^{2}

2W^{2} + W - 15 = 0

Factor:

(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 ft^{2}.

(5/2 ft)*(6 ft) = 15 ft^{2}

The answers work. L = 6 ft and W = 2.5 ft.

Bob