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An athlete is riding his bicycle along the boundaries of a square field starting from the corner point A. He reaches the corner point C located diagonally opposite to the starting point after riding for 30 minutes. If the speed of the athelete's bicycle is 8 km per hour, then what is the area of the field in square kilometers?
- a)4
- b)8
- c)12
- d)16
- e)36
Correct answer is option 'A'. Can you explain this answer?
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An athlete is riding his bicycle along the boundaries of a square fiel...
Understanding the Problem
To find the area of the square field, we need to determine the length of one side of the square.
Given Data
- Speed of the athlete = 8 km/h
- Time taken to reach point C = 30 minutes
Calculating Distance Travelled
1. Convert time from minutes to hours:
- 30 minutes = 30/60 hours = 0.5 hours
2. Calculate the distance covered by the athlete:
- Distance = Speed × Time
- Distance = 8 km/h × 0.5 h = 4 km
Understanding the Path
- The athlete rides from corner A to corner C, which are diagonally opposite corners of the square.
- In a square, the distance between two opposite corners (the diagonal) can be calculated using the formula:
\[ \text{Diagonal} = \text{Side} \times \sqrt{2} \]
Setting Up the Equation
- Let the side of the square be \( s \).
- Therefore, \( s \times \sqrt{2} = 4 \) km.
Solving for Side Length
1. Rearranging the equation:
- \( s = \frac{4}{\sqrt{2}} \)
2. Simplifying:
- \( s = \frac{4 \sqrt{2}}{2} = 2 \sqrt{2} \) km
Calculating Area of the Square
- The area \( A \) of the square is given by:
\[ A = s^2 \]
1. Substituting the value of \( s \):
- \( A = (2 \sqrt{2})^2 = 4 \times 2 = 8 \, \text{km}^2 \)
Conclusion
The area of the field is 8 square kilometers, but since the options provided state that the correct answer is option 'A', which is 4 square kilometers, the athlete must have taken a different route or the problem might contain an error in the options presented.
To find the area of the square field, we need to determine the length of one side of the square.
Given Data
- Speed of the athlete = 8 km/h
- Time taken to reach point C = 30 minutes
Calculating Distance Travelled
1. Convert time from minutes to hours:
- 30 minutes = 30/60 hours = 0.5 hours
2. Calculate the distance covered by the athlete:
- Distance = Speed × Time
- Distance = 8 km/h × 0.5 h = 4 km
Understanding the Path
- The athlete rides from corner A to corner C, which are diagonally opposite corners of the square.
- In a square, the distance between two opposite corners (the diagonal) can be calculated using the formula:
\[ \text{Diagonal} = \text{Side} \times \sqrt{2} \]
Setting Up the Equation
- Let the side of the square be \( s \).
- Therefore, \( s \times \sqrt{2} = 4 \) km.
Solving for Side Length
1. Rearranging the equation:
- \( s = \frac{4}{\sqrt{2}} \)
2. Simplifying:
- \( s = \frac{4 \sqrt{2}}{2} = 2 \sqrt{2} \) km
Calculating Area of the Square
- The area \( A \) of the square is given by:
\[ A = s^2 \]
1. Substituting the value of \( s \):
- \( A = (2 \sqrt{2})^2 = 4 \times 2 = 8 \, \text{km}^2 \)
Conclusion
The area of the field is 8 square kilometers, but since the options provided state that the correct answer is option 'A', which is 4 square kilometers, the athlete must have taken a different route or the problem might contain an error in the options presented.
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An athlete is riding his bicycle along the boundaries of a square field starting from the corner point A. He reaches the corner point C located diagonally opposite to the starting point after riding for 30 minutes. If the speed of the atheletes bicycle is 8 km per hour, then what is the area of the field in square kilometers?a)4b)8c)12d)16e)36Correct answer is option 'A'. Can you explain this answer?
Question Description
An athlete is riding his bicycle along the boundaries of a square field starting from the corner point A. He reaches the corner point C located diagonally opposite to the starting point after riding for 30 minutes. If the speed of the atheletes bicycle is 8 km per hour, then what is the area of the field in square kilometers?a)4b)8c)12d)16e)36Correct answer is option 'A'. Can you explain this answer? for GMAT 2024 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about An athlete is riding his bicycle along the boundaries of a square field starting from the corner point A. He reaches the corner point C located diagonally opposite to the starting point after riding for 30 minutes. If the speed of the atheletes bicycle is 8 km per hour, then what is the area of the field in square kilometers?a)4b)8c)12d)16e)36Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for GMAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An athlete is riding his bicycle along the boundaries of a square field starting from the corner point A. He reaches the corner point C located diagonally opposite to the starting point after riding for 30 minutes. If the speed of the atheletes bicycle is 8 km per hour, then what is the area of the field in square kilometers?a)4b)8c)12d)16e)36Correct answer is option 'A'. Can you explain this answer?.
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