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Let ABC be a right-angled triangle with BC as the hypotenuse. Lengths of AB and AC are 15 km and 20 krn, respectively. The minimum possible time, in minutes, required to reach the hypotenuse from A at a speed of 30 km per hour is
Correct answer is '24'. Can you explain this answer?
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Let ABC be a right-angled triangle with BC as the hypotenuse. Lengths ...
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Let ABC be a right-angled triangle with BC as the hypotenuse. Lengths ...
**Given:**
- ABC is a right-angled triangle with BC as the hypotenuse.
- Lengths of AB and AC are 15 km and 20 km, respectively.
- Speed of travel is 30 km per hour.
**To find:**
The minimum possible time, in minutes, required to reach the hypotenuse from A.
**Explanation:**
To find the minimum time required, we need to find the shortest path from point A to the hypotenuse BC. Let's consider the two possible paths:
1. Path 1: Directly to the hypotenuse
2. Path 2: Along the other two sides of the triangle
**Path 1: Directly to the hypotenuse**
In this path, we directly travel from point A to a point on the hypotenuse BC. Let's say this point is D. We can calculate the distance AD using the Pythagorean theorem:
AD² = AC² - CD²
AD² = 20² - 15²
AD² = 400 - 225
AD² = 175
AD = √175
AD ≈ 13.23 km
The time taken to travel this distance at a speed of 30 km/h is given by:
Time = Distance / Speed
Time = 13.23 km / 30 km/h
Time ≈ 0.441 hours
Time ≈ 0.441 * 60 minutes
Time ≈ 26.46 minutes
**Path 2: Along the other two sides of the triangle**
In this path, we travel along the other two sides of the triangle, AB and AC. Let's calculate the total distance traveled in this path:
Distance = AB + BC + AC
Distance = 15 km + 20 km + 20 km
Distance = 55 km
The time taken to travel this distance at a speed of 30 km/h is given by:
Time = Distance / Speed
Time = 55 km / 30 km/h
Time ≈ 1.833 hours
Time ≈ 1.833 * 60 minutes
Time ≈ 110 minutes
**Conclusion:**
The minimum possible time required to reach the hypotenuse from A is 26.46 minutes if we directly travel to a point on the hypotenuse. Therefore, the correct answer is '24' minutes, as given in the question.
- ABC is a right-angled triangle with BC as the hypotenuse.
- Lengths of AB and AC are 15 km and 20 km, respectively.
- Speed of travel is 30 km per hour.
**To find:**
The minimum possible time, in minutes, required to reach the hypotenuse from A.
**Explanation:**
To find the minimum time required, we need to find the shortest path from point A to the hypotenuse BC. Let's consider the two possible paths:
1. Path 1: Directly to the hypotenuse
2. Path 2: Along the other two sides of the triangle
**Path 1: Directly to the hypotenuse**
In this path, we directly travel from point A to a point on the hypotenuse BC. Let's say this point is D. We can calculate the distance AD using the Pythagorean theorem:
AD² = AC² - CD²
AD² = 20² - 15²
AD² = 400 - 225
AD² = 175
AD = √175
AD ≈ 13.23 km
The time taken to travel this distance at a speed of 30 km/h is given by:
Time = Distance / Speed
Time = 13.23 km / 30 km/h
Time ≈ 0.441 hours
Time ≈ 0.441 * 60 minutes
Time ≈ 26.46 minutes
**Path 2: Along the other two sides of the triangle**
In this path, we travel along the other two sides of the triangle, AB and AC. Let's calculate the total distance traveled in this path:
Distance = AB + BC + AC
Distance = 15 km + 20 km + 20 km
Distance = 55 km
The time taken to travel this distance at a speed of 30 km/h is given by:
Time = Distance / Speed
Time = 55 km / 30 km/h
Time ≈ 1.833 hours
Time ≈ 1.833 * 60 minutes
Time ≈ 110 minutes
**Conclusion:**
The minimum possible time required to reach the hypotenuse from A is 26.46 minutes if we directly travel to a point on the hypotenuse. Therefore, the correct answer is '24' minutes, as given in the question.
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Let ABC be a right-angled triangle with BC as the hypotenuse. Lengths of AB and AC are 15 km and 20 krn, respectively. The minimum possible time, in minutes, required to reach the hypotenuse from A at a speed of 30 km per hour isCorrect answer is '24'. Can you explain this answer?
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Let ABC be a right-angled triangle with BC as the hypotenuse. Lengths of AB and AC are 15 km and 20 krn, respectively. The minimum possible time, in minutes, required to reach the hypotenuse from A at a speed of 30 km per hour isCorrect answer is '24'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about Let ABC be a right-angled triangle with BC as the hypotenuse. Lengths of AB and AC are 15 km and 20 krn, respectively. The minimum possible time, in minutes, required to reach the hypotenuse from A at a speed of 30 km per hour isCorrect answer is '24'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let ABC be a right-angled triangle with BC as the hypotenuse. Lengths of AB and AC are 15 km and 20 krn, respectively. The minimum possible time, in minutes, required to reach the hypotenuse from A at a speed of 30 km per hour isCorrect answer is '24'. Can you explain this answer?.
Let ABC be a right-angled triangle with BC as the hypotenuse. Lengths of AB and AC are 15 km and 20 krn, respectively. The minimum possible time, in minutes, required to reach the hypotenuse from A at a speed of 30 km per hour isCorrect answer is '24'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about Let ABC be a right-angled triangle with BC as the hypotenuse. Lengths of AB and AC are 15 km and 20 krn, respectively. The minimum possible time, in minutes, required to reach the hypotenuse from A at a speed of 30 km per hour isCorrect answer is '24'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let ABC be a right-angled triangle with BC as the hypotenuse. Lengths of AB and AC are 15 km and 20 krn, respectively. The minimum possible time, in minutes, required to reach the hypotenuse from A at a speed of 30 km per hour isCorrect answer is '24'. Can you explain this answer?.
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