SOLUTION: A rancher wants to use 400 feet of fencing to enclose a rectangular area of 5100 square feet. What dimensions should the rectangle have?

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Question 935989: A rancher wants to use 400 feet of fencing to enclose a rectangular area of 5100 square feet. What dimensions should the rectangle have?
Found 3 solutions by josgarithmetic, lwsshak3, MathTherapy:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Dimensions x and y and are unknown.
A and p are known area and perimeter.

system%28xy=A%2C2x%2B2y=p%29

2y=p-2x
y=p%2F2-x
-
xy=A
x%28p%2F2-x%29=A
%28p%2F2%29x-x%5E2=A
px-2x%5E2=2A
-2x%5E2%2Bpx=2A
2x%5E2-px=-2A
2x%5E2-px%2B2A=0, you can probably factor the quadratic member when the values for p and A are used, but you do not always know. Examples vary.

x=%28p%2B-+sqrt%28p%5E2-4%2A2%2A2A%29%29%2F%282%2A2%29
highlight%28x=%28p%2B-+sqrt%28p%5E2-16A%29%29%2F%282%2A2%29%29

I leave the rest of the work and decisions to you.

Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
A rancher wants to use 400 feet of fencing to enclose a rectangular area of 5100 square feet. What dimensions should the rectangle have?
***
let x=width of rectangular area
length=(400-2x)/2=(200-x)
length*width=area
x(200-x)=5100
200x-x^2=5100
x^2-200x+5100=0
(x-170)(x-30)=0
x=170
or
x=30
200-x=170
What dimensions should the rectangle have?
width=30 ft
length=170 ft

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

A rancher wants to use 400 feet of fencing to enclose a rectangular area of 5100 square feet. What dimensions should the rectangle have?
Let length be L, and width, W

Since perimeter = 2(L + W), then: 2(L + W) = 400

2(L + W) = 2(200)

L + W = 200_____W = 200 – L -------- eq (i)

Since area = 5,100 sq ft, and area = LW, then it can be said that: L(200 – L) = 5,100

200L+-+L%5E2+=+5100

L%5E2+-+200L+%2B+5100+=+0

(L - 170)(L - 30) = 0

L – 170 = 0					OR					L - 30 = 0

L, or length = 170 feet			OR					L = 30



If length = 170, then width = 200 – 170, or 30 feet

If length = 30, then width = 200 – 30, or 170 feet



Therefore, dimensions of rectangle are: highlight_green%28system%28170_by%2C30%29%29  

You can do the check!! 

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