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# Let ABC be a right-angled triangle with BC as the hypotenuse. Lengths

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Math Expert
Joined: 02 Sep 2009
Posts: 64144
Let ABC be a right-angled triangle with BC as the hypotenuse. Lengths  [#permalink]

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02 Apr 2020, 09:33
00:00

Difficulty:

35% (medium)

Question Stats:

71% (03:05) correct 29% (03:39) wrong based on 21 sessions

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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:

A. 20
B. 21
C. 22
D. 23
E. 24

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Posts: 1832
Location: India
Re: Let ABC be a right-angled triangle with BC as the hypotenuse. Lengths  [#permalink]

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02 Apr 2020, 11:39
1
1
$$BC = \sqrt{AB^2 + AC^2}$$

$$BC = \sqrt{15^2 + 20^2} = 25$$

For minimum possible time, we have to cover the shortest distance from A to hypotenuse. {Shortest distance from a point to a line is the perpendicular distance)

1/2 *AB *AC = 1/2 *BC * AD

AD = $$\frac{15*20}{25}$$ = 12 Km

Time taken = $$\frac{12}{30} *60$$ = 24 mins

Bunuel wrote:
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:

A. 20
B. 21
C. 22
D. 23
E. 24

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Re: Let ABC be a right-angled triangle with BC as the hypotenuse. Lengths   [#permalink] 02 Apr 2020, 11:39