Final answer:
To find the dimensions of the rectangle, we can assign variables to the width and length. By setting up two equations using the given information, we can solve for the values of the variables and determine the dimensions of the rectangle. The width is 3.5 meters and the length is 4 meters.
Step-by-step explanation:
To solve this problem, we can start by assigning variables to the dimensions of the rectangle. Let's let 'w' represent the width of the rectangle and 'l' represent the length. We are given that the length is 3 meters less than twice the width, so we can write the equation: l = 2w - 3.
The area of a rectangle is found by multiplying the length by the width, so we can write another equation: lw = 14.
Substituting the expression for l from the first equation into the second equation, we get (2w - 3)w = 14. Expanding and rearranging, we have 2w^2 - 3w - 14 = 0. This quadratic equation can be solved using factoring, completing the square, or the quadratic formula. Once we find the values of w, we can substitute them back into the equation l = 2w - 3 to find the corresponding values of l.
Let's solve the quadratic equation:
- 2w^2 - 3w - 14 = 0
- (w + 2)(2w - 7) = 0
- w + 2 = 0 or 2w - 7 = 0
- w = -2 or w = 7/2
Since a negative width doesn't make sense in this context, we can ignore the solution w = -2. Therefore, the width of the rectangle is w = 7/2 = 3.5 meters. Substituting this value back into the equation l = 2w - 3, we find the length l = 2(3.5) - 3 = 4 meters.
Therefore, the dimensions of the rectangle are 3.5 meters by 4 meters.