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

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gamjatang
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Size of the room - Length = 12 - Width = 16 - Height = [#permalink] New post   25 Nov 2005, 06:23
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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: Size of the room - Length = 12 - Width = 16 - Height = [#permalink] New post   25 Nov 2005, 06:50
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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Re: Size of the room - Length = 12 - Width = 16 - Height = [#permalink] New post   25 Nov 2005, 06:57
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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Re: Size of the room - Length = 12 - Width = 16 - Height = [#permalink] New post   25 Nov 2005, 07:27
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 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



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Re: Size of the room - Length = 12 - Width = 16 - Height = [#permalink]
25 Nov 2005, 07:27
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