Answer:
5 ft
Step-by-step explanation:
Total area of turf and flower bed is [tex]1200\ \text{ft}^2[/tex]
Turf dimensions is 20 feet by 30 ft
Area of turf = [tex]20\times 30=600\ \text{ft}^2[/tex]
Area of flower bed = [tex]1200-600=600\ \text{ft}^2[/tex]
Let [tex]x[/tex] be the width of the flower bed so area of flower bed is
[tex]2\times 30x+2(20+2x)x=600\\\Rightarrow 30x+20x+2x^2=300\\\Rightarrow 2x^2+50x-300=0\\\Rightarrow x^2+25x-150=0\\\Rightarrow x=\dfrac{-25\pm \sqrt{25^2-4\times \:1\times \left(-150\right)}}{2\times \:1}\\\Rightarrow x=5,-30[/tex]
So, width of the flower bed is 5 ft.
