Answer:
[tex]$\large \boxed{\text{23 ft by 20 ft}}[/tex]
Step-by-step explanation:
Let x = the width of the garden
Then x + 3 = the length of the garden
Area of garden = length × width
A = lw = x(x+ 3)
[tex]\begin{array}{rcl}x( x+ 3)& = & 460\\x^{2} + 3x& = &460\\x^{2} + 3x - 460& = &0\\x + 23 = 0 & \text{or} & x - 20 = 0\\x = -23 & \text{or} & \mathbf{x = 20}\\\end{array}[/tex]
width = x = 20 ft
length = x + 3 = 20 +3 = 23 ft
[tex]\text{The dimensions of the garden are $\large \boxed{\textbf{23 ft by 20 ft}}$}[/tex]
Check:
[tex]\begin{array}{rcl}20(20 + 3) & = &460\\20(23) & = & 460\\460 & = & 460\\\end{array}[/tex]
OK.
