To enclose rectangular field whose area is 68200 square meter, a farmer used 1460 m of fencing material. What is the length and width of the field.

Please answer.. Thank you

L * w = 68200

however unless you know more about the ratio of L to w, there are an infinite number of solutions.

I did not notice the second part.

L * w = 68200
2 L + 2 w = 1460

L = 730 - w

(730-w)w = 68200

730 w - w^2 = 68200
w^2 -730 w + 68200 = 0
w = [ 730 +/- sqrt(532900-272800)]/2

w = [730 +/-510 ]/2
w = 110 or 620
L = 620 and w = 110

To find the length and width of the rectangular field, we need to solve a system of equations using the given information.

Let's assume the length of the field is L and the width is W.

The perimeter of a rectangle is given by the formula:
Perimeter = 2L + 2W

In this case, the farmer used 1460 meters of fencing material, which is equal to the perimeter of the rectangular field:
1460 = 2L + 2W

The area of a rectangle is given by the formula:
Area = L * W

In this case, the area of the rectangular field is 68200 square meters:
68200 = L * W

We now have a system of two equations:

1) 1460 = 2L + 2W
2) 68200 = L * W

Let's solve this system of equations to find the values of L and W.

From equation 1) we can rewrite it as:
730 = L + W

We can rearrange equation 2) to solve for L:
L = 68200 / W

Substituting this value of L in equation 1), we get:
730 = (68200 / W) + W

To solve for W, we can multiply both sides of the equation by W:
730W = 68200 + W^2

Rearranging the equation:
W^2 + 730W - 68200 = 0

Now we have a quadratic equation. We can solve it using factoring, completing the square, or the quadratic formula.

Using the quadratic formula:
W = (-b ± √(b^2 - 4ac)) / (2a)

In this case, a = 1, b = 730, and c = -68200.

Plugging in these values, we get:
W = (-730 ± √(730^2 - 4(1)(-68200))) / (2(1))

After solving this equation, we get two possible values for W. Let's call them W1 and W2.

Once we have the value(s) of W, we can substitute it back into equation L = 68200 / W to find the corresponding value(s) of L.

This will give us the length and width of the rectangular field.