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

To find the length and breadth of the rectangular field, we need to set up a quadratic equation based on the given information.

Let's assume the length of the field is x meters and the breadth is y meters.

We have two pieces of information:
1. The area of the field is 2000 sq.m, so xy = 2000.
2. The perimeter of the field is 180m, so 2x + 2y = 180.

Let's solve the quadratic equation step by step.

Step 1: Rearrange the second equation to express y in terms of x.
2x + 2y = 180
2y = 180 - 2x
y = 90 - x

Step 2: Substitute the value of y in terms of x into the first equation.
xy = 2000
x(90 - x) = 2000
90x - x^2 = 2000

Step 3: Rearrange the equation to standard quadratic form (ax^2 + bx + c = 0).
x^2 - 90x + 2000 = 0

Now, we can solve this quadratic equation by factoring, completing the square, or using the quadratic formula.

Factoring:
(x - 40)(x - 50) = 0

Setting each factor equal to zero:
x - 40 = 0 or x - 50 = 0

Solving for x:
x = 40 or x = 50

Since the length cannot be negative, we discard the solution x = 40.

Therefore, the length of the field is x = 50m.

To find the breadth, we can substitute the value of x into the equation y = 90 - x:
y = 90 - 50
y = 40m

Therefore, the length and breadth of the field are (50m, 40m).

The correct answer is option C) (40m, 50m).

To solve this problem, we need to form a quadratic equation using the given information about the area and perimeter of the rectangular field.

Let's start by considering the length of the field as x meters. Therefore, the breadth of the field will be (180 - 2x)/2 meters since the perimeter is given as 180 meters.

The area of a rectangle is given by the formula: Area = Length × Breadth

Substituting the given values, the area of the field is: 2000 sq. m = x × (180 - 2x)/2

To simplify this equation, we can multiply both sides by 2 to remove the fraction:
4000 sq. m = x × (180 - 2x)

Expanding the equation further:
4000 sq. m = 180x - 2x^2

Now, we have a quadratic equation in the standard form:
2x^2 - 180x + 4000 = 0

To solve this quadratic equation, we can either factorize it or use the quadratic formula. Since it might not be easy to factorize, let's use the quadratic formula:

The quadratic formula is given by: x = (-b ± √(b^2 - 4ac)) / (2a)

For our equation, a = 2, b = -180, and c = 4000.

Substituting the values into the quadratic formula:
x = (-(-180) ± √((-180)^2 - 4(2)(4000))) / (2(2))

Simplifying this equation further:
x = (180 ± √(32400 - 32000)) / 4
x = (180 ± √400) / 4
x = (180 ± 20) / 4

So, we have two possible solutions for x:
x1 = (180 + 20) / 4 = 200 / 4 = 50
x2 = (180 - 20) / 4 = 160 / 4 = 40

Therefore, the possible values for the length of the field are x = 50 meters and x = 40 meters.

Next, we need to find the breadth of the field by substituting these values back into the equation:
Breadth = (180 - 2x) / 2

Using x = 50,
Breadth1 = (180 - 2(50)) / 2 = 80 / 2 = 40 meters

Using x = 40,
Breadth2 = (180 - 2(40)) / 2 = 100 / 2 = 50 meters

Therefore, the possible values for the length and breadth of the field are:

A) (205m, 80m)
B) (50m, 40m)
C) (40m, 50m)
D) None

Hence, the correct answer is B) (50m, 40m).

x by (2000/x)

x + 2000/x = 90

x^2 - 90 x + 2000 = 0

(x-50)(x-40) = 0

I suspect it is longer than it is wide