<PRE><B>Question 191521</B>
first  problem

per  =  206  =  (2*l) +   (2*w)  =  2( w + 9)  +  2(w) =  2w  + 18  +  2w =  4w  +18

substr  18  from  both  sides

188  =  4w

divide  each  side  by  4

w =  47

check  per  =  206  =  2  (  47  +  (47 + 9)  )  =  206  ok

Area  =  l *  w  =  47  *  (  47  + 9)  =  47 * 56  =  2632

problem  2

area  =  l *  w  =  180  *  240  =  43200    

factory  area  is  then  43200  /  2  =  21600     as  is  green  belt  area

factory  dim  are  (  180-2w)  by  (240 -2w)  

factory  area  =  l*w  =  (180-2w)  *  (240-2w)

21600=180 *240 -2*180*w -2*240*w +4w^2

21600 = 43200 -360w -480w  +4w^2

subst  21600  both  sides

0  =  21600 -840w +4w^2

factor    0=  4( w^2  -210 w  +5400)

solve  using  quadratic  formula

w  =    (     -(-210)  +-  sq  rt  (   (-210)^2 - 4 (1) (5400)  )  )  /2 (1)

w=  (  210  +-  150  )  /2

w=   360/2=180   to  big   not  realistic

or  w =  60/2  =  30

this  makes  factory  size   (180-2*30)  =  120  by  (240  -2*30)  =  180

checking  180 * 120  =  21600  ok  </PRE>