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A rectangular prism has a total surface area of 56. Also, the sum of all the edges of the prism is 60. Find the length of the diagonal joining one corner of the prism to the opposite corner.

 Oct 5, 2021
 #1
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The length of the diagonal is 10*sqrt(2).

 Oct 5, 2021
 #2
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Wrong

Guest Oct 5, 2021
 #3
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Kinda messy, but here is my solution

 

w = width

s = side

 

Sum of edges =  4 w   +   8 s   = 60

                              w +      2s = 15

                                   w = 15 - 2s

 

 

Surface area =  s*s    + s*s   + w*s  + w*s + w*s + w*s   =  2s^2 + 4 ws = 56   

                                                                                             s^2 + 2ws = 28        sub in the red equation for w

                                   s^2 +2s (15-2s) = 28

                                  s^2 + 30s - 4s^2  - 28 = 0

                                    -3s^2 + 30s-28 = 0               Quadratic formula show s = 1.04189    or  8.95811 (throw out ....too big)

                                                                                                             then w = 15-2s = 12.91622

 

Now we have the dimensions of the 3-d solid      diagonal = sqrt ( s^2 + s^2 + w^2) =~~ 13 units

 Oct 5, 2021

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