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3 rectangular faces of a triangular prism have areas of 30, 40, 50. 2 triangular faces have a combined area of 12. What are the dimensions of the prism?

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You can deduce that the area of one of the triangles if 6.

You also know the triangle sides are in proportion of $3:4:5$ with each other. So you could say the lengths are $3x,4x,5x$.

Generally, from there you could use Heron's Formula to find the sides. But, knowing about triangles, you might be able to come up with the sides without using the formula.

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