Question 960803
L=length; W=width; P=perimeter=308 meters; A=area=5785 square meters
{{{P=2(L+W)}}}
{{{308m=2(L+W)}}} Divide each side by 2.
{{{154m=L+W}}}
{{{154m-W=L}}} Use this to substitute for L.
{{{A=LW}}}
{{{5785m^2=LW}}} Substitute for L.
{{{5785m^2=(154m-W)(W)}}}
{{{5785m^2=154W-W^2}}} Subtract 5785 sq m from each side.
{{{0=-W^2+154W-5785m^2}}}
{{{0=-1(W-65)(W-89)}}}
{{{W-65=0}}} or {{{W-89=0}}}
{{{W=65}}} or {{{W=89}}} ANSWER: The width is 89m or 65m.
{{{L=154m-W}}}
{{{L=154m-65m}}} or {{{L=154m-89m}}}
{{{L=89m}}} or {{{L=65m}}} ANSWER: The length is 65m or 89m.
The dimensions of the parking lot are 65 meters by 89 meters.
CHECK:
{{{A=LW}}}
{{{5785m^2=(65m)(89m)}}}
{{{5785m^2=5785m^2}}}