Logic for shortest distance to cover all area of rectangle

I have to start from a point on rectangle of area lxb, and want to detect a object of certain area less than that of rectangle, object is placed inside rectangle. I want to find the shortest distance to reach that object. if placed at a point I can check the area of about 'a' meters around me.strong text In what manner should I need to travel to reach that object in shortest time?

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