A rectangular plot of land has sides with lengths of 38 m and 52 m correct to the nearest m. Find th

JAMB Mathematics 2023 59 views

A rectangular plot of land has sides with lengths of 38 m and 52 m correct to the nearest m. Find the range of the possible values of the area of the rectangle

  1. 1957 m² ≤ A < 1995 m²
  2. 1931.25 m² ≤ A < 2021.25 m² ✓
  3. 1950 m² ≤ A < 2002 m²
  4. 1931.25 m² ≥ A > 2021.25 m²

Explanation

Step 1: Understand measurement precision
“Correct to nearest m” means true value within ±0.5 m
For 38 m: actual value is 37.5 ≤ length < 38.5
For 52 m: actual value is 51.5 ≤ width < 52.5

Step 2: Find minimum area
Use smallest possible dimensions
Minimum area = 37.5 × 51.5
= 1931.25 m²

Step 3: Find maximum area
Use largest possible dimensions
Maximum area = 38.5 × 52.5
= 2021.25 m²

Step 4: Write range correctly
Minimum is included (≤)
Maximum is not reached (<)
Therefore: 1931.25 ≤ A < 2021.25 m²

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