Math portfolio: Modeling a functional building The task is to design a roof structure for the given building. The building has a rectangular base 150 meters long and 72 meters wide. The height of the building should not exceed 75% of its width

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Math portfolio: Modeling a functional building

The task is to design a roof structure for the given building. The building has a rectangular base 150 meters long and 72 meters wide. The height of the building should not exceed 75% of its width for stability or be less than half the width for aesthetic purpose. The minimum height of a room in a public building is 2.5 meters.

The height of the structure ranges from 36m to 54 (72×75%) m as per the specification.

At first I will model a curved roof structure using the minimum height of the structure that is 36 meters.

From the diagram given, the curve roof structure seems to be a parabola hence I will use a general equation of parabola that is

y= ax2 + bx +c -----------(1)

Now the width of the structure is 72 meters and the height is 36 meters.

Let the coordinate of the left bottom corner of the base is (0,0)

Then the coordinate of the right bottom corner will be (72,0) and the coordinate of the vertex of the parabola will be (36,36)

Since the above three points lies