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A rectangular prism has a total surface area of $36.$  Also, the sum of all the edges of the prism is $32.$  Find the length of the diagonal joining one corner of the prism to the opposite corner.

 Aug 2, 2021
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x * y * 4   + y * y * 2  = 36      x = long side   y = short side length

 

4x + 8 y = 32       y = 4 -.5 x

 

 

x *(4-.5x) * 4    + (4-.5x)^2 * 2 = 36     expand then simplify, then

   Quadratic Formula  x = 4.77485       then y = 1.613          diagonal is then sqrt ( 1.613^2 + 1.613^2 + 4.775^2)  = sqrt (24 ) = 5.29

 Aug 2, 2021

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