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The dimensions are integers, so let's call them i, j, and k meters.

You have a situation where i*j = 24, i*k = 36, and j*k = 54. That's a relatively simple system of simultaneous equations to solve, even by direct trial. For example, i and j must be one the pairs 1 and 24, 2 and 12, 3 and 8 or 4 and 6. Looking at the other numbers the only ones that seem likely are 3 and 8 or 4 and 6, so try one of those and see if you can find a value of k that's consistent with that.

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Q: The dimensions of a rectangular prism are whole numbers. The areas of the faces are 24 m2 36 m2 and 54 m2. What are the dimensions of the prism?
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