Answer
10 feet by 15 feet
Work Step by Step
length = $x$
width = $y$
$xy=150$
$2x+2y=50$
$2x+2y=50$
$2x+2y-2y=50-2y$
$2x=50-2y$
$2x/2=(50-2y)/2$
$x=25-y$
$xy=150$
$(25-y)y=150$
$25y-y^2=150$
$25y-y^2-25y+y^2=150-25y+y^2$
$0=y^2-25y+150$
$0=(y-10)(y-15)$
$y-10=0$
$y-10+10=0+10$
$y=10$
$xy=150$
$x*10=150$
$x*10/10=150/10$
$x=15$
$y-15=0$
$y-15+15=0+15$
$y=15$
$xy=150$
$x*15=150$
$x*15/15=150/15$
$x=10$
