Answer
$\dfrac{25}{3}$ feet and $24$ feet
Work Step by Step
Let $x$ be the width of the garden. Then, $3x-1$ is the length of the garden. Using $A=lw$ or the formula for the area of a rectangle, then
\begin{array}{l}\require{cancel}
A=lw
\\
200=(3x-1)(x)
\\
200=3x^2-x
\\
3x^2-x-200=0
.\end{array}
Using the FOIL Method which is given by $(a+b)(c+d)=ac+ad+bc+bd,$ the expression above is equivalent to
\begin{array}{l}\require{cancel}
(3x-25)(x+8)=0
.\end{array}
Equating each factor to zero (Zero Product Property) then the solutions of the equation above are $
x=\left\{ -8,\dfrac{25}{3} \right\}
.$ Since $x$ is a measurement, then $x=\dfrac{25}{3}$ and $3x-1=24.$ Hence, the dimensions are $\dfrac{25}{3}$ feet and $24$ feet.
