Final answer:
The width of the farmer's rectangular paddock is 30 meters, and the length is 40 meters, both of which satisfy the condition that the paddock's area is 1200m² with the length being 10m longer than the width.
Step-by-step explanation:
The question involves a farmer's rectangular paddock where the length is 10m longer than the width, and its area is 1200m². To find the length and width, we can let the width be represented by w meters. Therefore, the length would be w + 10 meters. We know that the area A of a rectangle is given by the product of its length and width, so A = w × (w + 10).
We can set up the equation: w² + 10w = 1200. Solving this quadratic equation, we find possible values for w. After finding the width, we add 10 to get the length. The solutions must make sense in the context of the problem, so the width and length must be positive real numbers.
By using factoring or the quadratic formula, we find that the paddock's width w is 30 meters, and the length is w + 10, which equals 40 meters.