Question

bocso wishes to start a 200m sq. rectangular vegetable garden. since he has only 50 m barbed wire, he fences three sides of the rectangular garden letting his house wall act as the fourt side of the fence. find the dimensions of the garden.

Answer 1

area of the garden=l*b=200m sq.⇒eq.1
the length of barbed wire used=50m
barbed wire used n the garden=b+l+b=50m
2b+l=50
l=50-2b
by substitutig this in eq.1,
b(50-2b)=200
50b-2$b^{2}$=200
2$b^{2}$-50b+200=0
$b^{2}$-25b+100=0
$b^{2}$-20b-5b+100=0
b(b-20)-5(b-20)=0
(b-5)(b-20)=0
therefore
b=5 or
b=20

when b=5,
l=50-2b
 =50-2(5)
 =50-10=40m

when b=20,
l=50-2b
  =50-2(20)
  =50-40=10m

ans.the dimensions of the garden are 40X5or 20X10