Rob is helping to build the set for a school play. He needs to construct a multi-colored tetrahedron using cloth and bamboo. The process involves:

1. Fitting three lengths of bamboo together such that they meet at a common point and each pair of rods forms a right angle.
2. Cutting three additional bamboo lengths to connect the other ends of the initial rods.
3. Creating four triangular fabric pieces to cover the tetrahedron's faces: blue, red, green, and yellow.

The areas of the red, yellow, and green pieces are $60$, $20$, and $15$ square feet, respectively. If the blue piece is the largest of the four sides, determine the area of the blue piece in square feet.

Let's think step by step and output the final answer within \boxed{}.
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