Question 964104
.
L=length; W=width; P=perimeter=500yds; A=area=14400 sq yds
P=2(L+W)
500yds=2(L+W)
250yds=L+W
250yds-W=L Use this to substitute for L
{{{LW=A}}} Substitute for L from above.
{{{(250yds-W)(W)=14400yds^2}}}
{{{-W^2+250W=14400}}} Subtract 14400 from each side.
{{{-W^2+250W-14400=0}}} Multiply by -1.
{{{W^2-250W+14400=0}}}
{{{(W-160)(W-90)=0}}}
{{{W-160=0}}} {{{or}}} {{{W-90=0}}}
{{{W=160}}} {{{or}}} {{{W=90}}}
ANSWER: The length and width are 160 yds by 90 yds.
CHECK:
P=2(L+W)
500yds=2(160yds+90yds)
500yds=2(250yds)
500yds=500yds