Question 205954
Area  = Length  *  Width,,A=LW = 160,,,,,,,or  L=160/W
.
Perimeter = 2(L+W) ,,,,,P=2L +2W =52,,,,subst  from  above
.
52= 2(160/W) +2W,,,,,multiply  thru  by  "W"
.
52W = 320 +2W^2
.
2w^2 -52W +320 =0,,,,,divide  by  2
.
W^2 -26W +160 =0
.
solve  for  W,,,using  Quadratic  Formula
.
a=1,,,,b=(-26),,,c=160
.
W=[ -(-26) +/-sqrt{ (-26)^2 -4 (1)(160)}]/2(1)
.
W= [26 +/- sqrt{676 -640}]/2
.
W= [26 +/- 6]/2
.
w= 10,,16
,
solving  for  L=160/W,,,L= 16,10
.
Therefore,,,W=10,,,L=16,,,,,,by  convention  W less  than L
.
Check,  A= 10*16=160,,,ok
.
P=2(10+16)=2*26 = 52,,,,,ok
.