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Triangles

Let ABC be a ...

Question

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___

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Solution

Hypotenuse BC of right angled triangle $A B C = \sqrt{(20^{2} + 15^{2})} = 25 k m$ .
Perpendicular distance from point A to hypotenuse $B C = \frac{(20 \times 15)}{25} = 12 k m$
For minimum time, minimum distance should be taken which is perpendicular distance.
Hence, minimum time in minutes $= \frac{(12 \times 60)}{30} = 24$

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