A square playground has an area of 1 127.6164 square metres. If a man walks at a speed of 2 9/20 metres per minute, approximately how many minutes will he take to walk one complete round around the boundary of the playground?

Introduction / Context:

This question combines geometry and time and distance concepts. We are given the area of a square playground and the walking speed of a man in metres per minute. The task is to find the approximate time he takes to walk one complete lap around the boundary of the square. That means we must move from area to side length, then to perimeter, and finally relate perimeter to speed and time. Such multi step problems are very common in aptitude tests because they check multiple concepts together.

Given Data / Assumptions:

• The playground is exactly square in shape.
• Area of the square = 1 127.6164 square metres.
• Walking speed of the man = 2 9/20 metres per minute.
• 2 9/20 metres per minute can be converted to an improper fraction.
• We need the approximate time in minutes to walk once around the playground.

Concept / Approach:

For a square, area = side^2, so the side length is the square root of the area. Once we know the side length, we can compute the perimeter as 4 times the side. The total distance walked in one lap is this perimeter. Using the time, speed and distance relationship distance = speed * time, we rearrange to time = distance / speed. Because the numbers are not very simple, we approximate the square root and the final time to two decimal places, matching the style of the given options.

Step-by-Step Solution:

Verification / Alternative check:

To check the approximation, we can multiply the speed back by the time. Using 54.82 minutes at 2.45 metres per minute gives a distance of approximately 54.82 * 2.45 ≈ 134.32 metres, which matches the calculated perimeter. Also, 33.58 squared is very close to 1 127.6164, confirming that our side length is accurate. These checks show that the approximations are consistent and that 54.82 minutes is a reliable value.

Why Other Options Are Wrong:

Option 50.82 minutes corresponds to a shorter total distance when multiplied by 2.45 and would not reach the full perimeter of about 134.32 metres. Option 54.62 minutes is slightly smaller than 54.82 and leads to a smaller distance than needed. Option 50.62 minutes is also too small. Only 54.82 minutes, when multiplied by the walking speed, correctly reproduces the perimeter of the playground and aligns with the geometry of the square.

Common Pitfalls:

Learners often forget that the given area is for a square and attempt to use formulas for rectangles or circles. Another common error is to miscalculate the square root or to approximate it too coarsely, which leads to incorrect perimeters. Mistakes also occur when converting the mixed fraction 2 9/20 into an improper fraction or decimal. Carefully carrying each step, maintaining sufficient decimal accuracy and checking by multiplying back are good habits to avoid these issues.

Final Answer:

The man will take approximately 54.82 minutes to walk one round around the playground.