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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 \(56\). Find the length of the diagonal joining one corner of the prism to the opposite corner.

 Apr 23, 2022
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Surface area =    2 ( ab + bc + ac)  =  56  (1)

 

Length of the surface edges =  4 ( a + b + c)  =  56

So     a + b + c  =  14

Square both sides of this

a^2 + 2 ab + 2 ac + b^2 + 2 bc + c^2  = 196       rearrange as

a^2 + b^2 +c^2  + 2 (ab + bc + ac) =  196    (2)

 

Sub (1)  into (2)

 

a^2 + b^2  + c^2   +  56  =  196

 

a^2 + b^2 + c^2  =  140

 

Length   of the dagonal  =   sqrt [ a^2 + b^2 + c^2 ] =   sqrt (140) =  2sqrt (35)

 

 

cool cool cool

 Apr 23, 2022

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