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Problem of the Week
Problem E
Corner Connection

In rectangular prism \(ABCDEFGH\), the sum of the lengths of all of the edges is \(28\text{ cm}\), and the total surface area is \(13 \text{ cm}^2\).

The top face of the prism is rectangle ABCD. The bottom face is rectangle EFGH with vertex E directly below vertex A, F below B, G below C, and H below D.

What is the length of \(EC\), the diagonal of the prism?