Final answer:
Using the Pythagorean theorem and solving the quadratic equation based on the provided information, we determine that the correct dimensions of the field are a length of 18 meters and a width of 12 meters.
Step-by-step explanation:
The student is asking for the dimensions of a rectangular field given a relationship between the length and width and the measure of the diagonal. We can use the Pythagorean theorem to solve this question, which states that in a right-angled triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b).
If we let the width of the field be x meters, then the length would be x + 6 meters. Since the diagonal represents the hypotenuse of the triangle formed by the length and width of the field, we can write the equation as:
x^2 + (x + 6)^2 = 30^2
Solving the quadratic equation will give us the dimensions of the field. After simplifying the equations and solving for x, we find that x = 12 and therefore the length is 18 m and the width is 12 m. So the correct answer is:
d. Length = 18 m, Width = 12 m