91Ó°ÊÓ

Length of a rectangle is four feet less than twice the width.

The area of the rectangle is 200 square foot.

The area of a rectangle is:

$A=l×w$

Where, $l$is the length of the rectangle and $w$is the width of the rectangle. Using the given information, it is clear that $l=2w-4$. Substitute $l=2w-4$and $A=200$in the above formula.

$\begin{array}{rcl}200& =& (2w-4)w\\ 0& =& 2w^2-4w-200\\ 0& =& 2(w^2-2w-100)\\ 0& =& w^2-2w-100\end{array}$

Quadratic formula for the equation $a{x}^2+bx+c=0$is:

$x=\frac{-bÂ\pm \sqrt{b^2-4ac}}{2a}$

In the above quadratic equation $a=1,b=-2,c=-100$. Use the quadratic formula.

$\begin{array}{rcl}w& =& \frac{-(-2)Â\pm \sqrt{(-2{)}^2-4(1\left)\right(-100)}}{2\left(1\right)}\\ w& =& \frac{2Â\pm \sqrt{4+400}}{2}\\ w& =& \frac{2}{2}Â\pm \frac{2\sqrt{101}}{2}\\ w& =& 1Â\pm \sqrt{101}\\ w& =& 11.04987,-9.04987\end{array}$

Width cannot be a negative value. So, $w≈11$.

The lenght of the rectangle is:

$\begin{array}{rcl}l& =& 2w-4\\ & =& 2\left(11\right)-4\\ & =& 22-4\\ & =& 18\end{array}$

The length of the garden is approximately 18 feet and the width 11 feet.