Length = 10 m, width = 6 m. Inside is a square field with side half of length. Ratio of areas =

Appeared in: UP NHM CHO 7 Sept 2022 (Shift-2)

Explanation

First, calculate the area of the outer rectangular field: Area = Length × Width = 10 m × 6 m = 60 m².
Next, determine the dimensions and area of the inner square field. The side is half the rectangle's length, so Side = 10 m / 2 = 5 m. The square's area is Side × Side = 5 m × 5 m = 25 m².
Finally, form the ratio of the square's area to the rectangle's area, which is 25:60.
Simplify this ratio by dividing both numbers by their greatest common divisor, 5. This gives the final ratio of 5:12.

Option B: This is the inverted ratio of the rectangle's area to the square's area (60:25).
Option C: This ratio results from an incorrect calculation or simplification. It does not match the calculated ratio of 25:60.
Option D: This is the inverse of the incorrect option 5:3. It also stems from a calculation error.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Calculating the ratio of geometric areas (Rectangle and Square) as background academic context rather than a clinical decision trigger.
Numeracy skills are fundamental in nursing for accurate medication dosage calculation, where ratios and proportions are frequently used to ensure patient safety.
Understanding ratios is essential for interpreting lab results, mixing solutions (e.g., for wound irrigation), and calculating IV drip rates.
What if the square's side was half the rectangle's width instead? The side would be 6/2 = 3 m, and the area would be 9 m². The ratio would be 9:60, which simplifies to 3:20. This highlights the importance of carefully reading which dimension is being referenced.

How to Approach the Question

First, identify the geometric shapes mentioned in the problem: a rectangle and a square.
Note down the given dimensions: Rectangle length = 10 m, width = 6 m.
Use the formula for the area of a rectangle (Area = Length × Width) to find its area.
Determine the dimensions of the square based on the problem statement (side is half of the rectangle's length).
Calculate the area of the square using its formula (Area = Side × Side).
Form a ratio of the two calculated areas. By convention, this is typically the area of the inner shape to the area of the outer shape.

Concept Tested & Keywords

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Practise the full UP NHM CHO 7 Sept 2022 (Shift-2)

Attempt every question from this paper in a timed mock, then review the full solution for each one.