The area = L x W = 9
(x + 2) * ( 2x + 3) = 9 simplify
2x^2 + 4x + 3x + 6 = 9
2x^2 + 7x - 3 = 0
Using the quadratic formula to find both solutions
[ - 7 ± √ [ 7^2 - 4(2)(-3) ] ] -7 ± √[ 73]
_____________________ = ______________ take the positive solution ⇒ x ≈ .386 ft
2 (2) 2(2)
So the dimensions are = (.386 + 2) = 2.386 ft x (2(.386) + 3) = 3.772 ft
The perimeter = 2 [ 2.386 + 3.772 ] ≈ 12.316 ft