Let and be the vertices of a triangle . Then the maximum area of the parallelogram , formed with vertices and on the sides and of the triangle respectively, is .

Question

Let  and  be the vertices of a triangle . Then the maximum area of the parallelogram , formed with vertices  and  on the sides  and  of the triangle  respectively, is .

Canvas Classes · Accepted Answer

🧠 Why "Maximum Area" Whispers "Midpoints"

A parallelogram  shares vertex  with , with  on the three sides. The word maximum is the only hint the examiner gives — and for an inscribed parallelogram sharing one vertex, the maximum-area configuration is when  are exactly the midpoints of their respective sides. Worth memorising: this midpoint-theorem result reappears almost every other year.

🖼️ Visual Sketch

Picture  with the parallelogram  tucked inside, sharing the corner at . The midsegment

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