By using the concept of maxima, it can be calculated that
Length of the rectangle of perimeter 72 m with maximum area is 18 m
Breadth of the rectangle of perimeter 72 m with maximum area is 18 m
What is maxima of a function?
Maxima of a function gives the maximum value of the function in a given interval or in the whole domain.
Let the length of the rectangle be l m and width of the rectangle be w m
Perimeter (P) = 2(l + w)
By the problem,
2(l + w) = 72
l + w = [tex]\frac{72}{2}[/tex]
l + w = 36
w = 36 - l
Area (A) = l [tex]\times[/tex] w
A = l [tex]\times[/tex] (36 - l) = [tex]36l - l^2[/tex]
Differentiation with A with respect to l
[tex]\frac{dA}{dl} = 36 - 2l[/tex]
For maximum area,
[tex]\frac{dA}{dl} = 0[/tex]
36 - 2l = 0
2l = 36
l = [tex]\frac{36}{2}[/tex]
l = 18 m
[tex]\frac{d^2A}{dl^2} = -2 < 0[/tex]
Hence area is maximum
w = 36 - 18 = 18 m
Length of the rectangle of perimeter 72 m with maximum area is 18 m
Breadth of the rectangle of perimeter 72 m with maximum area is 18 m
To learn more about maxima of a function, refer to the link-
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