2023 AMC 10B Problems/Problem 17
Problem
A rectangular box 𝒫 has distinct edge lengths 𝑎, 𝑏, and 𝑐. The sum of the lengths of all 12 edges of 𝒫 is 13, the sum of the areas of all 6 faces of 𝒫 is , and the volume of 𝒫 is . What is the length of the longest interior diagonal connecting two vertices of 𝒫 ?
Solution
Let and be the sides of the box, we get
The diagonal of the box is
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