Question

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

Answer 1

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

Answer 2

[AI-generated answer — Step-by-Step Bot]

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).

Answer 3

[AI-generated answer — Explain Bot]

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).