Question

Help on #97! Need to know how to work it out using polynomial equations!

Answer 1

Area = length * width
length = (2 * width) - 1
$10 = l*w\\ 10=(2w-1)*w\\ 10=2w^{2}-w\\ 2w^{2}-w-10=0\\ (2w-5)(w+2)=0\\\\ 2w-5=0\\ 2w=5\\ w=\frac{5}{2}=2.5\\ w+2=0\\ w=-2$
Since length cannot be negative, w = -2 is not a solution. Thus, $\frac{5}{2}~ft$ is your width.
Since length = 2 * width - 1, plug in width:
$l=2(\frac{5}{2})-1\\ l=5-1\\ l=4~ft$