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For the following question:

Peter lives 12 miles west of school and Bill lives north of school.Peter finds the direct distance from his house to Bill is 6 miles shorter than the distance by way of shcool.How many miles north of school does Bil live?

For this after constructing a right triangle I got

-12x = 108 so x=-9 (distance from school to Bill) Does the - in the answer depict anything ?

Edit: My perpendicular was x and my hypotenuse was x-6

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    Your equation should be $12 x = 108$; no negative. The right triangle should have legs $12$ (west) and $x$ (north), and hypotenuse $(12+x)-6$ (six less than the two-leg trip by way of the school) which is $6+x$. (I suspect you used $x-6$.)2012-06-28
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    What i did was make the perpendicular X and since the hypotenuse was 6 less i made it x-6 and then applied the phythagoras. Is this wrong ?2012-06-28
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    The statement:the direct distance from his house to Bill is 6 miles shorter than the distance by way of shcool... implies direct distance = (x+12)-6(because via school he needs to travel to school 12 miles and then x miles from there to his friend).2012-06-28
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    I still cant really tell the difference..2012-06-28
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    @Rajeshwar: You may be misunderstanding the phrase "distance by way of school". This is NOT "distance to the school"; it's the distance *from one house to another*, along the route that stops at the school at the corner. That distance is $x+12$: the "$x$" takes you from one house to the school, and the "$12$" takes you from the school to the other house, completing the trip.2012-06-28
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    Hmm ok.. That makes sense so the hypotenuse will be ((12+x) - 6)2012-06-28

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Sides of right angle triangle are $x,12,x+6$.Using Pythagoras theorem, $x^2+12^2=(x+12)^2 \implies 144=12x+36 \implies 12x=108 \implies x=9$. There is no negative sign.You have made some sign mistake somewhere in your solution.

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    What i did was make the perpendicular X and since the hypotenuse was 6 less i made it x-6 and then applied he Pythagoras. Is this wrong ?2012-06-28
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    Distance between two houses via school= distance from peter's house to school+distance from school to bill's house=$12+x$ not just $x$.You need to subtract $6$ from $x+12$ not just $x$.2012-06-28