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Omni-MATH / Aaron has 144 identical cubes, each with edge length 1 cm. He uses all of the…

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Aaron has 144 identical cubes, each with edge length 1 cm. He uses all of the cubes to construct a solid rectangular prism, which he places on a flat table. If the perimeter of the base of the prism is 20 cm, what is the sum of all possible heights of the prism?

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