Answer
$[20,40]$
Work Step by Step
$2l+2w=120$, $w=60-l$.
$l\times w\geq800$.
$l\times(60-l)\geq800,$
$60l-l^2\geq800,$
$-l^2+60l-800\geq0,$
$-l^2+20l+40l-800\geq0,$
$-l(l-20)+40(l-20)\geq0,$
$(l-20)(40-l)\geq0,$
thus, cut points are: $l=20$ or $l=40$
$\begin{array}{lll}
Intervals&testingcases&(l-20)(40-l)&(l-20)(40-l)\geq0\\
(-\infty, 20) & 0 & (-)(+)=(-)&F\\
(20,40)&30&(+)(+)=(+)&T\\
(40,\infty)&50&(+)(-)=(-)&F
\end{array}$
Therefore, The Solution set are:
$[20,40]$
