Final answer:
To find the dimensions of the rectangle, set up an equation using the given information. Solve the quadratic equation to find the width and length of the rectangle. The dimensions of the rectangle are 6 meters by 19 meters.
Step-by-step explanation:
To find the dimensions of the rectangle, we need to set up an equation using the given information. Let's assume the width of the rectangle is x meters, then the length would be 2x + 7 meters. The formula for the area of a rectangle is length times width, so we have:
A = (2x + 7) * x = 99 m^2
Simplifying the equation, we get:
2x^2 + 7x - 99 = 0
Now, we can solve this quadratic equation. Factoring or using the quadratic formula, we find that x = 6 or x = -8. Since the width cannot be negative, the width of the rectangle is 6 meters. Substituting this value back into the equation, we find the length of the rectangle is 2(6) + 7 = 19 meters.
Therefore, the dimensions of the rectangle are 6 meters by 19 meters.