The right angled triangle PQR is to be constructed in the xy-plane, so that the right angle is at P and PR is parallel to the x-axis. The x and y coordinates of P,Q and R are to be integers that satisfy the inequality −4≤x≤5 and 6≤y≤16. 

 How many different triangles with these properties could be constructed? Please explain how you got your answer.

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