Asked by aarati
A man who has 144m of fencing material wishes to enclose a rectangular garden.Find the maximum area he encloses
Answers
Answered by
Damon
144/4 = 36
36*36 = 1296 m^2
now how did I know it was square?
2x+2y = p = perimeter
so
x+y = p/2
so
y = p/2-x
A = x y = x(p/2-x)
A = (p/2)x - x^2
or
x^2 - (p/2)x = - A
x^2 -(p/2)x + (p/4)^2 = -A + p^2/16
[ x - (p/4)]^2 = - (A-p^2/16)
so vertex at area = (p/4)^2
and x = y = p/4 so square
36*36 = 1296 m^2
now how did I know it was square?
2x+2y = p = perimeter
so
x+y = p/2
so
y = p/2-x
A = x y = x(p/2-x)
A = (p/2)x - x^2
or
x^2 - (p/2)x = - A
x^2 -(p/2)x + (p/4)^2 = -A + p^2/16
[ x - (p/4)]^2 = - (A-p^2/16)
so vertex at area = (p/4)^2
and x = y = p/4 so square
Answered by
uditkumar
Mathematics-ii solution
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