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ps(miles)

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Senior Manager
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ps(miles) [#permalink] New post 09 May 2004, 08:33
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Towns A and C are connected bya straight highway which is 60 miles long . The straight line distance between A and town B is 50 miles , and the striahgt line distnace from town B to town C is 50 miles . How many miles is it from town B to the point on the highway connecting towns A and C which is closest to town B?

30
40
50
30sqrt2
60
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 [#permalink] New post 09 May 2004, 09:10
40 miles.

The point O on line AC nearest to B is 30 miles away from towns A and C.
Since Ab = BC = 50 OB = sqrt( 50^2 - 30^2 ) = 40
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Re: ps(miles) [#permalink] New post 12 May 2004, 06:17
shubhangi wrote:
Towns A and C are connected bya straight highway which is 60 miles long . The straight line distance between A and town B is 50 miles , and the striahgt line distnace from town B to town C is 50 miles . How many miles is it from town B to the point on the highway connecting towns A and C which is closest to town B?

30
40
50
30sqrt2
60


height of the traingle ABC (corresponding to point B) = (BC^2 - (AC/2)^2)^1/2 = (50^2 - 30^2)^1/2 = 40.

B is the answer.
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 [#permalink] New post 12 May 2004, 07:14
Quickest way without solving is to have ABC in a right triangle. BC and BA are the two sides = 50 with AC the hypotenuse = 60. Cut across from B to AC dividing the hypotenuse in half = 30. Call this point T. The new triangle ATB is in the 3:4:5 ratio or 30:40:50.
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 [#permalink] New post 12 May 2004, 07:17
ndidi204 wrote:
Quickest way without solving is to have ABC in a right triangle. BC and BA are the two sides = 50 with AC the hypotenuse = 60. Cut across from B to AC dividing the hypotenuse in half = 30. Call this point T. The new triangle ATB is in the 3:4:5 ratio or 30:40:50.


Bravo, ndidi204! 3:4:5, 5:12:13 are widely known Pifagorian numbers.
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 [#permalink] New post 12 May 2004, 07:41
40 is right.. thanks guys for such simple solutions.
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  [#permalink] 12 May 2004, 07:41
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