The length of a rectangular field is 3 yards less than twice the width. If the area of the field is 104 squared yards, what are the dimensions of the field? The answer is W=8, L=13 How do you work it out to get the answer????

let the width be x

then length is 2x-3

x(2x-3) = 104
2x^2 - 3x - 104 = 0
(2x+13)(x-8) = 0
x = -13/2 or x = 8, but x has to be positive for width
x = 8

width is 8
length = 2(8) - 3 = 13

To find the dimensions of the rectangular field, we can use the given information.

Let's assume the width of the field is denoted as 'W' yards.

According to the given information, the length of the field is 3 yards less than twice the width. So, the length can be expressed as (2W - 3) yards.

The area of a rectangle can be calculated by multiplying the length and the width. In this case, the area is given as 104 square yards.

Therefore, we have the equation:
(W)(2W - 3) = 104

To solve this equation, we can follow these steps:

1. Distribute the W to the expression (2W - 3):
2W^2 - 3W = 104

2. Move all terms to one side to create a quadratic equation:
2W^2 - 3W - 104 = 0

3. To solve this equation, we can either factor it or use the quadratic formula.

By factoring, we look for two numbers that multiply to give -208 (product of the coefficient of W^2 and the constant term -104) and add up to -3 (coefficient of W).
The two numbers are -13 and 16.
So, we can factor the equation as:
(2W - 13)(W + 8) = 0

Setting each factor to zero gives two possible solutions:
2W - 13 = 0 or W + 8 = 0

Solving these equations will give the possible values for the width:
2W = 13 or W = -8

From these equations, we get two possible values for the width:
W = 13/2 or W = -8

Since width cannot be negative, we can discard the second solution.

Therefore, W = 13/2 or W = 6.5.

However, since the width of a field cannot be a fraction, the width of the field is 6.5 yards is not a valid solution.

Thus, the only valid solution is W = 13/2.

Now, we can substitute this value back into the expression for length:
Length = 2W - 3 = 2(13/2) - 3 = 13 - 3 = 10.

Therefore, the width of the field is 13/2 yards (which can be simplified to 6.5 yards) and the length of the field is 10 yards.

So, the dimensions of the field are width = 6.5 yards and length = 10 yards.

It seems that the answer you provided (W = 8 and L = 13) is not correct.