Solve Quadratic Equation?

Question

To enclose a rectangular field whose area is 68,200 square meter, a farmer used 1,146 m. of fencing material. Find the leanght and width of the field.

Pls. solve this quickly and pls. show your solution. thanks to answers.

Answer 1

Let sides be x and y
xy = 68200
2x + 2y = 1146
2y = 1146 - 2x
y = 573 - x
x(573 - x) = 68200
x² - 573 x + 68200 = 0
x = [ 573 ±√(573² - 272800) ] / 2
x = (573 + 235) / 2 , x = (573 - 235) / 2
x = 404 , x = 169
y = 169 , y = 404

length = 404 m
breadth = 169 m

Answer 2

The given first:

1. Area: 68,200 sq m
2. Perimeter: 1,146 m

Deriving the Quadratic Equation:

3. We can get: (l + w) by dividing the perimeter into two:
1,146 / 2 = 573 m

l + w = 573 m
w = 573 - l (our 1st equation)

lw = 68,200 sq m (our 2nd equation)

substitute for w in the 2nd equation using the 1st equation

lw = 68,200
l(573-l) = 68,200
573l - l = 68,200
l² -573l + 68,200 = 0 (take note the signs are reversed)

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Using a calculator you will get the following values:
-168.67703958905122 and
-404.3229604109488

But I doubt that that's the answer your teacher wants but this is what you're going to get using the quadratic equation and it doesn't look pretty. I think you can use absolute values but not round them up to whole numbers: 168.68 and 404.32.

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However, there's another way with the same result:

Step 1: Take half the sum of the length and width (we'll call this the half-sum): 573 / 2 = 286.5

Step 2: Square the half-sum: 82,082.25.

Step 3: Subtract the area: 68,200 - 82,082.25 = 13,882.25

Step 4: Take the square root: 117.823

Length is half-sum + square root: 404.32

Width is half-sum - square root: 168.68

Answer 3

perimeter = 2(L + W)

2(L + W) = 1146

area = L * W

LW = 68200

Solve for L Or W in the area formula. I did W.

W = 68200/L (fraction)

Substitute W from area formula into perimeter formula.

2 ( L + 68200/L) = 1146

Solve for L now.

Distributive Property

2L + 136400/L= 1146

Get rid of fractions by multiplying every term by L.

2 L (squared) + 136400 = 1146L

move everything to one side

2 L (squared) - 1146L + 136400 = 0

now do quadratic equation.

You should get 404.3 and 168.7

Answer 4

x(squared) - 573x + 68 200 = 0 find x......... the two solutions are the width and the length

Answer 5

Area = lengthXbreadth
perimeter = 2(length+breadth)

=2(area/breadth + breadth)

=> perimeter Xbreadth = 2Xarea + (breadth)^2

solve for breadth as area and perimeter are known