To solve the problem, we need to use the following area formula:Area of a triangle = (1/2) x base x heightWe have to find out the relation between the line segment PQ and PR. We can determine this using the given information that the areas of triangles APQS and APRS are equal.Let's begin by calculating the area of triangle APQS and APRS using the above formula. We know that the height of both triangles is PS. Thus:Area of triangle APQS = (1/2) x PQ x PSArea of triangle APRS = (1/2) x PR x PSThe areas of both triangles are equal. Thus we have:(1/2) x PQ x PS = (1/2) x PR x PSWe can now cancel PS from both sides and simplify the equation. This gives:PQ = PRTherefore, the correct answer is (A) PQ = PR.