Step 1: Recall the Neighbourhood Unit concept.
Clarence Arthur Perry proposed the Neighbourhood Unit concept in 1929 as a model for planning residential areas around a walkable radius, sized so that children could reach school without crossing a busy arterial road.
Step 2: Recall the specific size and population figures Perry used.
Perry sized the unit for a population of about 5,000 people, matched to the enrollment of a single elementary school. He fixed the maximum walking distance from any dwelling to the school at a quarter mile, that is, 0.25 miles, roughly 400 metres. This distance was chosen because it was a comfortable walking distance for a young child, keeping the whole neighbourhood within about a 5 to 10 minute walk of the school at its centre.
Step 3: Check why the other values do not fit.
0.5 miles, 1 mile, and 1.5 miles are all larger than the distance Perry specified. Using any of these would place some households too far from the school for a small child to walk comfortably, and would not match the historical figure used in Perry's original 1929 proposal.
Final Answer:
Perry fixed the walking radius to the elementary school at a quarter mile.
\[ \boxed{0.25 \text{ miles, option (A)}} \]