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Sagot :
Answer:
400 m^2.
Step-by-step explanation:
The largest area is obtained where the enclosure is a square.
I think that's the right answer because a square is a special form of a rectangle.
So the square would be 20 * 20 = 400 m^2.
Proof:
Let the sides of the rectangle be x and y m long
The area A = xy.
Also the perimeter 2x + 2y = 80
x + y = 40
y = 40 - x.
So substituting for y in A = xy:-
A = x(40 - x)
A = 40x - x^2
For maximum value of A we find the derivative and equate it to 0:
derivative A' = 40 - 2x = 0
2x = 40
x = 20.
So y = 40 - x
= 40 - 20
=20
x and y are the same value so x = y.
Therefore for maximum area the rectangle is a square.
The largest area of rectangle will be 400 square meters.
Let us consider the length and breadth of rectangle is x and y respectively.
Perimeter of rectangle is given that 80 meters.
[tex]2x+2y=80\\\\x+y=40\\\\y=40-x[/tex]
Area of rectangle is,
[tex]=x*y\\\\=x*(40-x)\\\\A=40x-x^{2}[/tex]
For maximum area, differentiate Area with respect to x and equate with zero.
[tex]\frac{dA}{dx} =\frac{d}{dx}(40x-x^{2} ) \\\\\frac{dA}{dx} =40-2x=0\\\\x=40/2=20m[/tex]
So, [tex]y=40-20=20m[/tex]
Area = [tex]20*20=400m^{2}[/tex]
Thus, The largest area of rectangle will be 400 square meters.
Learn more:
https://brainly.com/question/20628915
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