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Distance problem

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by oks » Sun May 17, 2009 1:44 pm
. Dan and Karen, who live 10 miles apart meet at a cafe that is directly north of Dan’s house and directly east of Karen’s house. If the cafe is 2 miles closer to Dan’s house than to Karen’s house, how many miles is the cafe from Karen’s house?
(A) 6
(B) 7
(C) 8
(D) 9
(E) 10

OA: C
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by truplayer256 » Sun May 17, 2009 2:32 pm
From the diagram, we can clearly see that the pythagorean theorem can be applied to find the value of x (The distance from Karen's home to the cafe).

x^2+(x-2)^(2)=100
x^2+x^2-4x+4=100
2x^2-4x-96=0
2(x^2-2x-48)=0
2(x-8)(x+6)=0
x-8=0
x=8

C[/img]
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by tdadic84 » Mon May 18, 2009 6:46 am
The way I did it...

Once you figure out the triangle is 10, x, x-2 like the diagram above (should not be too hard, if it is, let me know), and you look at the answer choices, since you know it is a right angle triangle, just know the 10-8-6 rule and that is your answer.

Hence c
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