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?
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.