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2023 AMC 10B Problem 17

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2023 AMC 10B Problem 17AMC 10 Step by Step

Name: Date: September 13, 2026

Algebraic Manipulation · difficulty 3 of 5 · about 3 min · position P16-20

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 $\dfrac{11}{2}$ , and the volume of $P$ is $\dfrac{1}{2}$ . What is the length of the longest interior diagonal connecting two vertices of $P$ ?

A)
$2$
B)
$\frac{3}{8}$
C)
$\frac{9}{8}$
D)
$\frac{9}{4}$
E)
$\frac{3}{2}$

2023 AMC 10B Problem 17

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