We can substitute the value of L from the first equation into the second equation:
(2W + 3)W = 99
Distribute and simplify:
2W^2 + 3W = 99
Rearrange the equation to make it a quadratic equation:
2W^2 + 3W - 99 = 0
To solve this quadratic equation, we can use factoring, completing the square, or the quadratic formula. Let's use the quadratic formula:
W = (-b Β± β(b^2 - 4ac)) / (2a)
For our equation, a = 2, b = 3, and c = -99. Substituting these values into the quadratic formula:
W = (-3 Β± β(3^2 - 4(2)(-99))) / (2(2))
Simplifying further:
W = (-3 Β± β(9 + 792)) / 4
W = (-3 Β± β801) / 4
To find the approximate values of W, we need to evaluate the square root:
W β (-3 + β801) / 4 β 5.39
W β (-3 - β801) / 4 β -11.89
Since the width cannot be negative, we can discard the negative value of W. Therefore, the width is approximately 5.39.
To find the length (L), we can substitute this value back into the first equation:
L = 2W + 3 β 2(5.39) + 3 β 13.77
Therefore, the dimensions of the rectangle to the nearest thousandth are width = 5.39 m and length = 13.77 m.