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# If A is 25 kilometers east of N. which is 12 kilometers sout

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If A is 25 kilometers east of N. which is 12 kilometers sout [#permalink]  03 May 2017, 02:47
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Question Stats:

88% (01:48) correct 11% (03:29) wrong based on 26 sessions

If A is 25 kilometers east of B, which is 12 kilometers south of C, which is 9 kilometers west of D, how far is it. in kilometers. from A to D?

A) $$20$$

B)$$5\sqrt{34}$$

C) $$5\sqrt{41}$$

D) $$10 \sqrt{13}$$

E) $$71$$
[Reveal] Spoiler: OA

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Re: If A is 25 kilometers east of N. which is 12 kilometers sout [#permalink]  22 Sep 2017, 07:05
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Given the instructions, the figure is a trapezoid with larger base 25km long, smaller base 17km long and height 12km long. We are asked to find the oblique side. In order to find it we can exploit the fact that drawing the height DH we get a triangle whose hypotenuse is AD. Thus, using Pitagora's theorem we get $$sqrt(12^2+18^2)$$ that is not equal to 20.
In order to be 20 the number under the square root should be 400. Thus, CD must be equal to 9 so that AH is equal to 16.
Is there a typo or am I wrong in my computations?
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Re: If A is 25 kilometers east of N. which is 12 kilometers sout [#permalink]  22 Sep 2017, 07:36
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IlCreatore wrote:
Given the instructions, the figure is a trapezoid with larger base 25km long, smaller base 17km long and height 12km long. We are asked to find the oblique side. In order to find it we can exploit the fact that drawing the height DH we get a triangle whose hypotenuse is AD. Thus, using Pitagora's theorem we get $$sqrt(12^2+18^2)$$ that is not equal to 20.
In order to be 20 the number under the square root should be 400. Thus, CD must be equal to 9 so that AH is equal to 16.
Is there a typo or am I wrong in my computations?

Your reasoning is correct, even I landed up with the same solution.
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Re: If A is 25 kilometers east of N. which is 12 kilometers sout [#permalink]  25 Sep 2017, 04:28
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Just found the original source of the question there was a typo in the statement "which is 9 kilometers west of D".

Fixed
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Re: If A is 25 kilometers east of N. which is 12 kilometers sout [#permalink]  29 Sep 2017, 04:43
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Re: If A is 25 kilometers east of N. which is 12 kilometers sout [#permalink]  29 Sep 2017, 06:58
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IlCreatore wrote:
Just found the original source of the question there was a typo in the statement "which is 9 kilometers west of D".

Fixed

Thanks. Often these questions are difficult to figure out as they are written, they are not clear. Thank you so much for the fixing.

Back to the question

Attachment:

direction.jpg [ 10.1 KiB | Viewed 1686 times ]

BE 9, AE= 16, and DE= 12. Finally, DA= 20, because right triangle AED is a 3-4-5 triangle in which each side is multiplied by 4. If you don't realize that, use the Pythagorean theorem to get DA $$(DA)^2 = (AE)^2 + (DE)^2 = 256 + 144 = 400$$

DA = 20.
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Re: If A is 25 kilometers east of N. which is 12 kilometers sout   [#permalink] 29 Sep 2017, 06:58
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# If A is 25 kilometers east of N. which is 12 kilometers sout

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