The length of a rectangular field is 2m greater than three times its width. The area of the field is 1496 metre square. What are the dimensions of the field ?

w(3w+2) = 1496

y= 160

Let's assume the width of the field is 'w' meters.

According to the given information, the length of the field is 2 meters greater than three times its width, which can be expressed as:

Length = 3w + 2 meters

The area of a rectangle is calculated by multiplying its length and width. So, we can set up the following equation:

Area = Length × Width

Substituting the values, we get:

1496 = (3w + 2) × w

Now, let's solve the equation step by step:

1. Expand the equation:

1496 = 3w² + 2w

2. Rearrange the equation in standard form:

3w² + 2w - 1496 = 0

3. We can solve this quadratic equation by factoring, completing the square, or using the quadratic formula. In this case, let's use the quadratic formula:

w = (-b ± √(b² - 4ac)) / (2a)

Where a = 3, b = 2, and c = -1496. Substituting these values, we have:

w = (-2 ± √(2² - 4 × 3 × -1496)) / (2 × 3)

4. Simplify the equation:

w = (-2 ± √(4 + 17952)) / 6

w = (-2 ± √17956) / 6

5. Calculate the square root:

w = (-2 ± 134) / 6

w₁ = (−2 + 134) / 6 = 132 / 6 = 22

w₂ = (−2 - 134) / 6 = -136 / 6 = -22.67 (Discard this value as width cannot be negative)

Therefore, the width of the field is 22 meters.

6. Now, substitute the value of width (w) in the equation for length:

Length = 3w + 2
Length = 3 × 22 + 2
Length = 66 + 2
Length = 68

So, the dimensions of the field are 22 meters (width) and 68 meters (length).

To find the dimensions of the rectangular field, we need to solve the problem using algebra. Let's start by assigning variables to the unknowns.

Let's assume that the width of the field is "w" meters. Then, according to the given information, the length of the field is "3w + 2" meters, since it is 2 meters greater than three times the width.

We know that the area of a rectangle is found by multiplying its length by its width. In this case, the area is given as 1496 square meters.

So, we can set up the equation:
Area = Length × Width
1496 = (3w + 2) × w

To solve the equation, we can simplify it by multiplying the terms on the right side:
1496 = 3w^2 + 2w

Now, rearrange the equation to put it in standard quadratic form:
3w^2 + 2w - 1496 = 0

To solve quadratic equations, we can factorize, complete the square, or use the quadratic formula. In this case, let's use the quadratic formula to find the values of "w".

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

In our equation, a = 3, b = 2, and c = -1496. Substituting these values into the quadratic formula and simplifying, we get:
w = (-2 ± √(2^2 - 4*3*(-1496))) / (2*3)

Now, calculate the expression under the square root:
w = (-2 ± √(4 + 17952)) / 6
w = (-2 ± √17956) / 6

Simplifying further, we get:
w = (-2 ± 134.06) / 6

We have two possible solutions for "w":
w = (134.06 - 2) / 6 ≈ 22.34
w = (-134.06 - 2) / 6 ≈ -22.34 (since width cannot be negative)

Since dimensions cannot be negative, we can discard the negative value.

Therefore, the width of the field is approximately 22.34 meters.

To find the length of the field, substitute the value of "w" back into the expression for length:
Length = 3w + 2
Length = 3(22.34) + 2
Length = 67.02 + 2
Length ≈ 69.02

So, the dimensions of the rectangular field are approximately 22.34 meters by 69.02 meters.