Minimum Time to Hypotenuse

Question

Let $ABC$ be a right-angled triangle with $BC$ as the hypotenuse. Lengths of $AB$ and $AC$ are $15	ext{ km}$ and $20	ext{ km}$, respectively. The minimum possible time, in minutes, required to reach the hypotenuse from $A$ at a speed of $30	ext{ km}$ per hour is:

Accepted Answer

24. Shortest distance from $A$ to hypotenuse $BC$ is the altitude $h$ to $BC$. $BC = \sqrt{15^2 + 20^2} = 25	ext{ km}$. $h = \frac{AB 	imes AC}{BC} = \frac{15 	imes 20}{25} = 12	ext{ km}$. Time required = $\frac{12}{30}	ext{ hours} = 0.4	ext{ hours} = 24	ext{ minutes}$.

Answer

No other option is correct for this question.

Minimum Time to Hypotenuse

Explanation

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