2023 AMC 12B Problems/Problem 13
Problem
A rectangular box P has distinct edge lengths ,
, and
. The sum of the lengths of all
edges of P is
, the areas of all 6 faces of P is
, and the volume of P is
. What is the length of the longets interior diagonal connecting two vertices of P?
Solution 1 (algebraic manipulation)
We can create three equationss using the given information.
We also know that we want
. We know that
.
. So
. So our answer is
.