# Prism

The lenght, width and height of a right prism are 17, 11 and 11 respectively. What is the lenght of the longest segment whose endpoints are vertices of the prism?

Result

d =  23.043

#### Solution:

$a = 17 \ \\ b = 11 \ \\ c = 11 \ \\ \ \\ d^2 = a^2+b^2+c^2 \ \\ \ \\ d = \sqrt{ a^{ 2 }+b^{ 2 }+c^{ 2 } } = \sqrt{ 17^{ 2 }+11^{ 2 }+11^{ 2 } } = 3 \ \sqrt{ 59 } \doteq 23.0434 = 23.043$

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