(please explain with brief explanation)

The area of a rectangular field is 2000 sq.m and its perimeter is 180m. Form a quadratic equation by taking the length of the field as x and solve it to find the length and breadth of the field. the length and breadth are A) (205m, 80m) B) (50m, 40m) C) (40m, 50m) D)None

length = x

width = 2000/x

2x + 2 (2000/x) = 180

x + 2000/x = 90

x^2 + 2000 = 90 x

x^2 - 90 x + 2000 = 0

To solve this problem, we need to find the length and breadth of the rectangular field.

Let's assume the length of the field is "x" meters.
Since we know the area of the field is 2000 sq.m, the product of the length and breadth should be 2000. Therefore, the breadth can be calculated as:
breadth = 2000 / x

Now, let's calculate the perimeter.
Perimeter of a rectangle is given by the formula: P = 2(length + breadth).
In this case, the perimeter is 180m. Plugging in the values, we get:
180 = 2(x + 2000 / x)

Simplifying the equation, we have:
90 = x + 1000 / x

To get rid of the fraction, we multiply both sides of the equation by x:
90x = x^2 + 1000

Rearranging the equation, we have a quadratic equation:
x^2 - 90x + 1000 = 0

Now, we can solve this quadratic equation to find the length and breadth of the field.
Using factoring, the factors of 1000 are (20, 50) and (40, 25).
From these factors, we can see that the roots of the quadratic equation are x = 40 and x = 25.
Since the length cannot be smaller than the breadth, we can discard x = 25.
Therefore, the length of the field is 40m, and the breadth is 2000 / 40 = 50m.

Thus, the correct answer is C) (40m, 50m).