SOLUTION: A farmer has 800 metres of wire with which to fence 3 rectangular paddocks side by side. The width of the paddocks is x metres and the sum of their lengths is y metres. a)show th

Question 1118629: A farmer has 800 metres of wire with which to fence 3 rectangular paddocks side by side. The width of the paddocks is x metres and the sum of their lengths is y metres.
a)show that the total area of the paddocks is given by A= 400x-2x^2
b) find the greatest area that can be enclosed
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
A farmer has 800 metres of wire with which to fence 3 rectangular paddocks side by side.
The width of the paddocks is x metres and the sum of their lengths is y metres.
a)show that the total area of the paddocks is given by A= 400x-2x^2
4x + y = 800
y = -4x + 800
therefore
(-4x+800) = -2x+400 = the length (L)
:
A = width * length
A = x*(-2x+400)
A = -2x^2 + 400x
:
:
b) find the greatest area that can be enclosed
The above is a quadratic equation, max area is on the axis of symmetry
x = b/(2a), where a=-2, b = 400
x =
x = +100 m is the width for max area
Find the length
L = -2x + 400
L = -2(100) + 400
L = 200 is the length
Max area: 100 * 200 = 20,000 sq meters

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