Final answer:
The width of the parking lot is found to be approximately 146 feet by applying the Pythagorean theorem, which indicates none of the provided multiple-choice options are correct.
Step-by-step explanation:
The width of a rectangular parking lot is 53 ft less than its length. If it measures 250 ft diagonally, then we can determine the dimensions of the parking lot by applying the Pythagorean theorem which states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. This principle can be used since the width, length, and diagonal of a rectangle form a right-angled triangle.
Let x be the length of the parking lot. Then the width would be x - 53 feet. The Pythagorean theorem gives us x2 + (x - 53)2 = 2502. Simplifying this, we have x2 + x2 - 106x + 2809 = 62500, which simplifies to 2x2 - 106x - 59691 = 0. This is a quadratic equation that can be solved using factoring, the quadratic formula, or a calculator.
Upon solving, we find that x is approximately 199 feet (rounding to the nearest whole number), which makes the width 199 - 53 feet, or 146 feet. Therefore, none of the options (a) 5 ft, (b) 10 ft, (c) 15 ft, or (d) 20 ft are correct.