Respuesta :
Answer:
area = 1500× 750 = [tex]1125000 m^2[/tex]
Step-by-step explanation:
we know area of rectangle
for length = l m
and width = b m
[tex]A = lb[/tex]
and perimeter
[tex]Perimeter = 2 (length + width)[/tex]
but one side length measures is not required because of the river so
He does not use the fence along the side of the river
so we use this formula
Perimeter = P = L + 2 b
Perimeter is 3000 m
[tex]so \ \ 3000 = l +2b[/tex]
[tex]l = 3000 - 2b[/tex]
so area will be
[tex]A = (3000-2b)b[/tex]
it is a quadratic function whose max or min will
occur at the average of the Solutions.
on Solving (3000 - 2b)b = 0
3000 - 2b = 0 or b=0
2b =3000
[tex]b =\frac{3000}{2} \\b = 1500 m[/tex]
or [tex]b = 0 m[/tex]
The average of the values are [tex]\frac{(0+1500)}{2} = 750[/tex]
so for max area we use b= [tex]750 m[/tex]
The Length is then L=3000 - 2(750) = 3000 - 1500 = 1500
for max area
length = 1500 m
bredth = 750 m
area = 1500× 750 = [tex]1125000 m^2[/tex]
