Final answer:
The measures of the length and width of the rectangle are: Length: 24 meters, Width: 42 meters.
Step-by-step explanation:
To solve this problem, let's denote the length of the rectangle as 'L' and the width as 'W'. According to the problem, the area of the rectangle is 1008 square meters. We also know that the width is six meters less than twice the length, so we can write the equation: W = 2L - 6.
Substituting this value of W into the formula for area, we have: LW = 1008. Plugging in the expression for W, we get L(2L - 6) = 1008.
Simplifying and rearranging the equation, we have 2L^2 - 6L - 1008 = 0. This is a quadratic equation, which can be solved using factoring, completing the square, or the quadratic formula. By factoring, we can write (2L + 42)(L - 24) = 0. Setting each factor equal to zero, we find two possible lengths: L = -21 (not realistic in this context) and L = 24.
Since the problem stated that the length is a positive value, the length is 24 meters. Substituting this value back into the equation for the width, we find that the width is 2(24) - 6 = 42 meters.
Therefore, the measures of the length and width of the rectangle are: Length: 24 meters, Width: 42 meters.