80 m of fencing is available to enclose the rectangular garden of mangosteen give a function a that can represent the area that can be enclosed in terms of x
Answers
Given : 80 m of fencing is available to enclose the rectangular garden of mangos
To Find : give a function a that can represent the area that can be enclosed in terms of x
x is Length of rectangle
Solution:
Length = x
Breadth = y
Perimeter = 2(Length + Breadth )
= 2x + 2y
2x + 2y = 80
=> x + y = 40
=> y = 40 - x
Area of rectangle = Length . breadth
= xy
= x(40 - x)
= 40x - x²
Area of rectangle = 40x - x²
where x is the length of rectangle
to find maximum area
A = 40x - x²
dA/dx = 40 - 2x
40 - 2x = 0
=> x = 20
d²A/dx² = - 2 < 0
Hence Area is maximum when x = 20
maximum area = 40x - x² = 40*20 - 20² = 400 m²
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