Question 252661: FIND THE DIMENSIONS OF A RECTANGLE WHOSE PERIMETER IS 76CM THAT WILL GIVE THE MAXIMUM AREA.
Answer by palanisamy(496)   (Show Source):
You can put this solution on YOUR website! Let x and y be the sides of the rectangle.
Then, its perimeter 2x+2y = 76
2y = 76-2x
y = (76-2x)/2
y = 38-x ...(1)
The area of the rectangle is
A = xy
A = x(38-x)
A = 38x-x^2
Differentiating with respect to x,
dA/dx = 38-2x
For maximum or minimum value of A,
dA/dx = 0
38-2x = 0
2x = 38
x = 38/2
x = 19
Sustituting in (1), we get
y = 38-19 = 19
Therefore the dimensions are 19,19
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