What does the negative in this anwer depict.

Question

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

Answer 1

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.