Question 492709: A farmer has 120 meter of fence material. He wants to build a vegetable garden. If he uses all the material.
Here is the question
If the garden is to be near along barn which can be used as fence for one side of the garden, what is the biggest area that he can cultivate if the dimensions are also in whole numbers?
I need the answer immediately..
Thanks in advance :)
Answer by cleomenius(959)   (Show Source):
You can put this solution on YOUR website! We are going to set up a
quadratic equation, so we can make use of the formula to find the vertex of a parabola.
Let x = Width
let 2x = length
x + 2x = 120
width = (120 - 2x)
Area = x(120 - 2x)
Area = -2x^2 + 120x.
This is a parabola.
The formula for the vertex of a parabola is -b/2a.
since a < 0, there is a maximum at x.
-(120)/-2 (2) = 30.
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Now, if we were using all four sides, the maximum area would be 30 times 30 for 900.
but since we have one side of the river, we can use the maximum are for the length parallel to the river as 60, the width is still 30.
In effect your dimensions are 2 30 sides for the width and a 60 side for the length, basically what you have are two squares side by side forming a rectangle.
30 * 60 = 1800 meters for your maximum area.
Cleomenius.
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