The dimension of the rectangle with perimeter 92 m whose area is as large as possible is 23m by 23m
What is area and perimeter of a rectangle?
The perimeter of a rectangle is boundary surrounded by its four sides or sum of lengths and widths.
Perimeter of rectangle = 2(l + b)
Area is the surface covered by the figure.
Area of rectangle = l x b
According to the given question:
If the perimeter of a rectangle is 92m, hence
2(x + y) = 92
x is the length
y is the width
x + y = 46 ---- 1)
If the area is as large as possible, hence;
xy = maximum ----- 2)
From equation 1), x = 46 - y
Substitute into the second equation
(46-y)y = P(y)
P(y) = 46y - y²
If the product is at the maximum, hence;
dP/dy = 46 - 2y = 0
46 - 2y = 0
2y = 46
y = 23
Since x + y = 46
x = 46 - y
x = 46 - 23
x = 23
Hence the dimension of the rectangle with perimeter 92 m whose area is as large as possible is 23m by 23m.
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