Final answer:
The original side length of the square garage was approximately 18 feet. After a 50% increase in floor space, the new side length became about 22 feet, resulting in an approximate 22.22% increase in the length of one side. Options A-D do not accurately represent these calculations.
Step-by-step explanation:
The student's question involves finding the original and new side lengths of a square garage after a 50% increase in floor space, as well as calculating the percent increase in the length of one side.
To find the original side length, we take the square root of the original area, which is ∙330 square feet. The square root of 330 is approximately 18.17 feet. However, since we are looking for a whole number side length, we must round to the nearest whole number, which is 18 feet, since 18^2 = 324 and 19^2 = 361, which is too large. Now, with a 50% increase in floor space, the new area is 330 * 1.5 = 495 square feet. Taking the square root of this new area gives us the new side length of approximately 22.25 feet, which is closest to a whole number of 22 feet since 22^2 = 484 and 23^2 = 529, which is too large.
The percent increase in the length of one side is calculated by the formula: (new length - original length) / original length * 100. So, (22 feet - 18 feet) / 18 feet * 100 = ≄8/18 * 100 ≄ 22.22%. The closest answer to these calculations is not represented in options A-D, indicating a typo or error in the options presented.