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Ricardo lives 4 kilometers due west of Pat's house. Ann lives 6 kilome

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Ricardo lives 4 kilometers due west of Pat's house. Ann lives 6 kilome [#permalink]

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New post 01 Aug 2017, 13:38
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Ricardo lives 4 kilometers due west of Pat's house. Ann lives 6 kilometers due north of Pat's house, and 4 kilometers due west of David's house. What is the straight-line distance, in kilometers, from Ricardo's house to David's house?

(A) 4
(B) 5
(C) 8
(D) 10
(E) 12
[Reveal] Spoiler: OA

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Re: Ricardo lives 4 kilometers due west of Pat's house. Ann lives 6 kilome [#permalink]

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New post 01 Aug 2017, 14:09
Bunuel wrote:
Ricardo lives 4 kilometers due west of Pat's house. Ann lives 6 kilometers due north of Pat's house, and 4 kilometers due west of David's house. What is the straight-line distance, in kilometers, from Ricardo's house to David's house?

(A) 4
(B) 5
(C) 8
(D) 10
(E) 12




The 2 right triangles will form with base 4 and height 3

using pythagorus

D)

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Re: Ricardo lives 4 kilometers due west of Pat's house. Ann lives 6 kilome [#permalink]

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New post 01 Aug 2017, 22:24
Bunuel wrote:
Ricardo lives 4 kilometers due west of Pat's house. Ann lives 6 kilometers due north of Pat's house, and 4 kilometers due west of David's house. What is the straight-line distance, in kilometers, from Ricardo's house to David's house?

(A) 4
(B) 5
(C) 8
(D) 10
(E) 12

A........4........D
.
.
.
6
.
.
.
R.......4.......P

This is equivalent to



A........4........D
. .
. .
. .
6 .
. .
. .
. .
R.......4.......P.................X


RX = RP + AD = 8
XD = PA = 6
RD = SQRT (RX^2 + XD^2) = 8
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Re: Ricardo lives 4 kilometers due west of Pat's house. Ann lives 6 kilome [#permalink]

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New post 02 Aug 2017, 08:24
The straight line from Ricardo's to David's house will form two right triangles, splitting the distance between Ann's and Pat's houses in equal. Applying Pythagoras theorem we get the distance at 10.

Hence D. 10

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Re: Ricardo lives 4 kilometers due west of Pat's house. Ann lives 6 kilome   [#permalink] 02 Aug 2017, 08:24
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