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In the figure above, two searchlights S1 and S2 are located 10,000 feet apart; each covers an area of radius 10,000 feet, and each is located 8,000 feet from the railroad track. To the nearest 1,000 feet, what is the total length x of track spanned by the searchlights?
(A) 24,000
(B) 22,000
(C) 20,000
(D) 16,000
(E) 12,000
Attachment:
Searchlight.JPG [ 20.57 KiB | Viewed 17711 times ]
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See attached figure, all numbers are in 1000s.
Since height is 8 and hypotenuse is 10, side will be 6, by Pythagoras theorem.
x = 6000 (left of S1) + 10,000 (distance between S1 and S2) + 6,000 (right of S2)
x = 22,000
Option B
Since height is 8 and hypotenuse is 10, side will be 6, by Pythagoras theorem.
x = 6000 (left of S1) + 10,000 (distance between S1 and S2) + 6,000 (right of S2)
x = 22,000
Option B
Attachments
Capture1.JPG [ 39.03 KiB | Viewed 16926 times ]
General Discussion
16 Dec 2018, 07:18
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Hi Gmatprep550,
PRS1 is right angle triangle as R is 90 degree.
as given in the question and shown in the snapshot below,
PS1 = 10,000
RS1 = 6,0000
According to Pythagorean Theorem,
(PS1)^2 = (PR)^2 + (RS1)^2
(10,000)^2 = (PR)^2 + (8000)^2
PR = 6000, similarly, UV = 6000
You see S1S1 = 10,000 = RU
PR + RU + UV = x
6000 + 10000 + 6000 = x
22000 = x
hence B is correct.
PRS1 is right angle triangle as R is 90 degree.
as given in the question and shown in the snapshot below,
PS1 = 10,000
RS1 = 6,0000
According to Pythagorean Theorem,
(PS1)^2 = (PR)^2 + (RS1)^2
(10,000)^2 = (PR)^2 + (8000)^2
PR = 6000, similarly, UV = 6000
You see S1S1 = 10,000 = RU
PR + RU + UV = x
6000 + 10000 + 6000 = x
22000 = x
hence B is correct.
Attachments
Sanswer.JPG [ 35.58 KiB | Viewed 15771 times ]
kungfury42
Joined: 07 Jan 2022
Last visit: 31 May 2023
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18 Feb 2022, 08:43
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HKD1710
Drop perpendiculars from S1 and S2 to the track
Let Distance from the feet of the perpendicular to the extreme end be \(x\)
Then \(x^2 + {8k}^2 = {10k}^2\)
Hence, \(x = 6k\)
Therefore total coverage \(= 6k + 10k + 6k = 22k\)
Option B.
