An appraiser is analyzing a 2.5-acre rectangular lot that measures 250 feet in width. What is the depth of the lot?
Correct Answer
A) 436 feet
First convert acres to square feet: 2.5 × 43,560 = 108,900 sq ft. Then divide by width: 108,900 ÷ 250 = 435.6 feet, which rounds to 436 feet.
Why This Is the Correct Answer
Option A is correct because it follows the proper mathematical sequence for solving area problems. First, convert 2.5 acres to square feet: 2.5 × 43,560 = 108,900 square feet. Then, using the formula Area = Length × Width, solve for depth: 108,900 ÷ 250 = 435.6 feet. Rounding to the nearest whole foot gives 436 feet, which matches option A. This demonstrates the correct application of unit conversion and geometric problem-solving skills essential for appraisal work.
Why the Other Options Are Wrong
Option B: 348 feet
Option B (348 feet) represents an incorrect calculation, possibly from using the wrong conversion factor or making an arithmetic error in the division step, resulting in a depth that would create a lot area significantly smaller than 2.5 acres.
Option C: 522 feet
Option C (522 feet) is incorrect and would result in a lot area larger than 2.5 acres when multiplied by the 250-foot width, indicating either an error in the conversion from acres to square feet or incorrect application of the area formula.
Option D: 290 feet
Option D (290 feet) is incorrect and represents a significant underestimation of the lot depth, which would result in a total area of only about 1.66 acres rather than the given 2.5 acres.
The '4-3-5-6-0' Acre Memory Method
Remember 43,560 as 'Four-Three-Five-Six-Zero' by thinking: 'For (4) Three (3) Square (5) Measurements, Six (6) Zeros (0)' - this helps recall that 1 acre = 43,560 square feet. Then use 'Area Divided by Width = Depth' (A÷W=D).
How to use: When you see an area conversion problem, immediately write '43,560' at the top of your scratch work, multiply by the number of acres, then divide by the known dimension to find the unknown dimension.
Exam Tip
Always double-check your work by multiplying your calculated depth by the given width to verify it equals the total square footage - this reverse calculation catches most arithmetic errors.
Common Mistakes to Avoid
- -Forgetting to convert acres to square feet before calculating
- -Using an incorrect conversion factor (like 43,000 instead of 43,560)
- -Confusing which dimension to divide by (dividing by depth instead of width)
Concept Deep Dive
Analysis
This question tests the fundamental skill of converting between different units of area measurement and applying basic geometric formulas to determine property dimensions. Real estate appraisers must frequently work with lot measurements in both acres and square feet, requiring fluency in the conversion factor of 43,560 square feet per acre. The problem involves a two-step calculation: first converting the given acreage to square feet, then using the area formula (Area = Length × Width) to solve for the unknown dimension. This type of calculation is essential for property valuation, zoning compliance, and development feasibility analysis.
Background Knowledge
Appraisers must know that one acre equals exactly 43,560 square feet, a conversion factor derived from the historical definition of an acre as 660 feet by 66 feet. Understanding basic geometric formulas, particularly that Area = Length × Width for rectangles, is fundamental to property measurement and valuation work.
Real-World Application
Appraisers regularly encounter this type of calculation when analyzing irregular lots, verifying property descriptions, determining building coverage ratios, or assessing whether a property meets minimum lot size requirements for zoning compliance.
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