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Size of the room - Length = 12 - Width = 16 - Height =

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Size of the room - Length = 12 - Width = 16 - Height = [#permalink] New post 25 Nov 2005, 05:23
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Size of the room

- Length = 12
- Width = 16
- Height = 10

On the middle of the ceiling, there is a light.

What is the maximum length between the light and the corner of the room?
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Re: PS - Light in a room [#permalink] New post 25 Nov 2005, 05:50
gamjatang wrote:
Size of the room

- Length = 12
- Width = 16
- Height = 10

On the middle of the ceiling, there is a light.

What is the maximum length between the light and the corner of the room?


the longest distance from the light is from it to one of the four lower/floor corner of the room , called D
the distance from the light to one corner of the ceiling = 1/2 sqrt( 12^2+16^2) = 10
D= sqrt (10^2+ height^2) = 10sqrt2
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 [#permalink] New post 25 Nov 2005, 05:57
Consider this as two right triangles.

1st take the floor. The mid point is with length 6 and width 8. So From corner to midpoint on floor = sqrt ( 8 * 6) = 10.
Now height is 10. From corner to midpoint on floor is 10.
So corner to midpoint on ceiling is 10 sqrt(2)
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 [#permalink] New post 25 Nov 2005, 06:27
We need to do a little three dimentional speculation here. The hypotnuse of the ceiling is 12^2+16^2=sqrt400=20 since the light is in the middle, half the hypotnuse to <any> corner is 10. Use the height of the room as the leg and half the hypotnuse as the other leg and dropping the new hypotnuse down to the corner. 10^2+10^2=sqrt200=10sqrt2
  [#permalink] 25 Nov 2005, 06:27
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Size of the room - Length = 12 - Width = 16 - Height =

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