word problem, help please!
- Thread starter Kim
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The following recent threads cover this problem:
. . . . .Three sides of rectangle are 260 feet long
. . . . .Three sides of rectangle are 192 feet long
The number used is different, but the methodology is the same.
Eliz.
. . . . .Three sides of rectangle are 260 feet long
. . . . .Three sides of rectangle are 192 feet long
The number used is different, but the methodology is the same.
Eliz.
mmm4444bot
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- Oct 6, 2005
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My Take On It.
Hello Kim:
Hopefully you understand the diagram from the link that Elizabeth provided (the one with 192 feet and the river).
In your problem, the river is replaced by a barn.
Let x be the length of the two sides of the rectangle which touch the barn.
Since there is only 480 feet of fence available, the length of the side opposite of the barn has to be 480 - 2*x.
Hopefully you know that the area of this rectangle is:
A = x*(480 - 2*x)
Use the distributive property to simply:
A = -2*x^2 + 480*x
This is a quadratic equation of the form y = a*x^2 + b*x + c.
The graph of this area function is a parabola that opens downward. Therefore, the y-coordinate of the vertex represents the largest area.
The vertex occurs when x = -b/(2*a).
In your area equation, b = 480 and a = -2.
x = -b/(2*a) = 120.
This is one dimension. The side opposite the barn is 480 - 2*x. Substitute 120 for x.
480 - 2*120 = 240.
So, the dimensions of the rectangle are 240 feet by 120 feet.
Let us know if you need more help with this problem.
~ Mark
Hello Kim:
Hopefully you understand the diagram from the link that Elizabeth provided (the one with 192 feet and the river).
In your problem, the river is replaced by a barn.
Let x be the length of the two sides of the rectangle which touch the barn.
Since there is only 480 feet of fence available, the length of the side opposite of the barn has to be 480 - 2*x.
Hopefully you know that the area of this rectangle is:
A = x*(480 - 2*x)
Use the distributive property to simply:
A = -2*x^2 + 480*x
This is a quadratic equation of the form y = a*x^2 + b*x + c.
The graph of this area function is a parabola that opens downward. Therefore, the y-coordinate of the vertex represents the largest area.
The vertex occurs when x = -b/(2*a).
In your area equation, b = 480 and a = -2.
x = -b/(2*a) = 120.
This is one dimension. The side opposite the barn is 480 - 2*x. Substitute 120 for x.
480 - 2*120 = 240.
So, the dimensions of the rectangle are 240 feet by 120 feet.
Let us know if you need more help with this problem.
~ Mark