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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 km, 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...
The length of the altitude from A to the hypotenuse will be the shortest distance.
This is a right triangle with sides 3 : 4 : 5.
Hence, the hypotenuse = 
= 25 Km.
Length of the altitude = 15 x 20 / 25 = 12 Km
(This is derived from equating area of triangle, 15.20/2 = 25⋅altitude / 2)
The time taken = 12/30 x 60 = 24 minutes
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Let ABC be a right-angled triangle with BC as the hypotenuse. Lengths...
Finding the Minimum Time to Reach the Hypotenuse
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.
Approach:
To find the minimum time, we need to determine the shortest path from A to the hypotenuse BC. This can be done by finding the perpendicular distance from point A to the hypotenuse.
Solution:
Step 1: Finding the Length of the Hypotenuse BC
Using the Pythagorean theorem, we can find the length of the hypotenuse BC.
BC² = AB² + AC²
BC² = 15² + 20²
BC² = 225 + 400
BC² = 625
BC = √625
BC = 25 km
Step 2: Finding the Perpendicular Distance from A to BC
Let D be the point on BC such that AD is perpendicular to BC.
Using the formula for the area of a triangle, we can find the perpendicular distance AD.
Area(ABC) = 1/2 * AB * AC
Area(ABC) = 1/2 * 15 * 20
Area(ABC) = 150 square km
Area(ABC) = 1/2 * AD * BC
150 = 1/2 * AD * 25
AD = 150 * 2 / 25
AD = 12 km
Step 3: Finding the Time Required
To find the time required, we need to calculate the distance traveled along the hypotenuse BC.
Let's assume the distance traveled from A to D is x km.
Then, the distance traveled from D to C is (25 - x) km.
Total time = (Distance traveled from A to D / Speed) + (Distance traveled from D to C / Speed)
Total time = (x / 30) + ((25 - x) / 30)
Total time = (x + (25 - x)) / 30
Total time = 25 / 30
Total time = 5/6 hour
Total time = (5/6) * 60 minutes
Total time = 50 minutes
Answer:
The minimum possible time required to reach the hypotenuse from A at a speed of 30 km per hour is 50 minutes.
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.
Approach:
To find the minimum time, we need to determine the shortest path from A to the hypotenuse BC. This can be done by finding the perpendicular distance from point A to the hypotenuse.
Solution:
Step 1: Finding the Length of the Hypotenuse BC
Using the Pythagorean theorem, we can find the length of the hypotenuse BC.
BC² = AB² + AC²
BC² = 15² + 20²
BC² = 225 + 400
BC² = 625
BC = √625
BC = 25 km
Step 2: Finding the Perpendicular Distance from A to BC
Let D be the point on BC such that AD is perpendicular to BC.
Using the formula for the area of a triangle, we can find the perpendicular distance AD.
Area(ABC) = 1/2 * AB * AC
Area(ABC) = 1/2 * 15 * 20
Area(ABC) = 150 square km
Area(ABC) = 1/2 * AD * BC
150 = 1/2 * AD * 25
AD = 150 * 2 / 25
AD = 12 km
Step 3: Finding the Time Required
To find the time required, we need to calculate the distance traveled along the hypotenuse BC.
Let's assume the distance traveled from A to D is x km.
Then, the distance traveled from D to C is (25 - x) km.
Total time = (Distance traveled from A to D / Speed) + (Distance traveled from D to C / Speed)
Total time = (x / 30) + ((25 - x) / 30)
Total time = (x + (25 - x)) / 30
Total time = 25 / 30
Total time = 5/6 hour
Total time = (5/6) * 60 minutes
Total time = 50 minutes
Answer:
The minimum possible time required to reach the hypotenuse from A at a speed of 30 km per hour is 50 minutes.
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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 km, 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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