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x + y = 50 A = x y = x(50 - x ) = 50 x - x^2 let x be width and y be length ,and as we know perimeter of rectangle=2(length+width) let x be width and y be length ,and as we know perimeter of rectangle=2(length+widith) thanks a lot! Thank you so much5 answers
so
y = 50 -x
dA/dx = 0 for max or min = 50 -2x
2 x = 50
x = 25
so it is a square 25 on a side.
so 2(x+y)=100
x+y=50 , x=50-y
area=length*width
area=xy=(50-y)y
area=50y-y^2
dA/dy=0 for min or max
dA/dy=50-2y=0
y=25
x=25
so 2(x+y)=100
x+y=50 , x=50-y
area=length*width
area=xy=(50-y)y
area=50y-y^2
dA/dy=0 for min or max
dA/dy=50-2x=0
y=25
x=25
The area of a rectangle is defined as the total space occupied by it and perimeter is defined as the total length of the boundary of the rectangle.
Answer: The dimensions of the rectangle with a perimeter of 100m, and as large an area as possible, are 25 m and 25 m.
Area of rectangle = length × breadth
Perimeter of a rectangle = 2 (length + breadth)
Explanation:
Let 'A' be area and 'P' be perimeter of the rectangle
Let 'x' be the width and 'y' be the length
We know that,
Perimeter = 2 (length + breadth)
Hence,
P = 2(x+y)
=> 100 = 2(x+y) (Since, Perimeter = 100m)
=> x + y = 50
=> y = 50 - x ----------------------------- (1)
We know that,
Area of a rectangle = Length × Breadth
Hence,
A = xy -------------------(2)
By substituting the value of y from equation (1) to equation (2) we get,
Area = x(50 - x )
Area A(x) = 50 x - x2
Computing the derivative of A(x) we get,
A'(x) = 50 - 2x
Finding the critical points,
50 - 2x = 0
=> 2 x = 50
=> x = 25
Substitute x = 25 in equation (1)
We get,
y = 50 - x
=> y = 25