Math geometry

An architect is designing an A-frame cottage for a resort. A cross section of the cottage is an isosceles triangle. The front wall of the cottage must accommodate a sliding door.
Knowing that the architect is allowed a rectangular space of 240 m³ in volume to build inside, and the cottage should be 10 m long, determine the width and the height of the cottage that minimizes the cost of the building material, then determine the dimentions of the door with the maximum area.

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