Question 957710
A=area=840ft^2; P=perimeter=122ft; L=length; W=width
P=2(L+W) 
122ft=2(L+W) Divide each side by 2.
61ft=L+W Subtract W from each side
61ft-W=L
{{{A=L*W}}} Substitute for L
{{{840ft^2=(61ft-W)(W)}}}
{{{840ft^2=-W^2+61W}}} Subtract 840ft^2 from each side.
{{{0=-W^2+61W-840ft^2}}} Multiply by (-1)
{{{0=W^2-61W+840ft^2}}}
{{{0=(W-21)(W-40)}}}
{{{W-21=0}}} or {{{W-40=0}}}
{{{W=21ft}}} or {{{W=40ft}}} ANSWER 1: The width is 21 feet.
L=61ft-W=61ft-21ft=40ft ANSWER 2: The length is 40 feet.
CHECK:
A=L*W
840ft^2=(40ft)(21ft)
840ft^2=840ft^2