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Question 20 :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: [TITA]


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Explanatory Answer

Method of solving this CAT Question from Geometry
CAT 2017 Question Paper Quants Slot 1 Geometry

Given that ABC be a right-angled triangle with BC as the hypotenuse.
Lengths of AB and AC are 15 km and 20 km, respectively.
We have to find the minimum possible time, in minutes, required to reach the hypotenuse from A at a speed of 30 km per hour.
We should first find the minimum distance in order to find the minimum possible time, in minutes, required to reach the hypotenuse from A at a speed of 30 km per hour.
Therefore minimum distance AD has to be found and then it should be divided by the 30 km per hour.
Using the idea of similar triangles
Area of the triangle ABC
⟹ \\frac{1}{2}) × BA × AC = \\frac{1}{2}) × BC × AD
⟹ \\frac{1}{2}) × 15 × 20 = \\frac{1}{2}) × 25 × AD
⟹ AD = 12 units
Hence 12 kms is travelled at 30km per hour ⟹ \\frac{12}{30}) = \\frac{2}{5})
The minimum possible time, in minutes, required to reach the hypotenuse from A at a speed of 30 km per hour is \\frac{2}{5}) × 60 = 24 minutes
Key thing to be noted here is using Pythagoras theorem to find the altitude AD and then using Speed, Time and Distance formula to find the time.

The question is "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: [TITA]"

Hence, the answer is 24

 

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