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Let $ABCDEFGH$ be right rectangular prism. The total surface area of the prism $15.$ Also, the sum of all the edges of the prism is $17.$ Find the length of the diagonal joining one corner of the prism to the opposite corner.

 May 29, 2024
 #1
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Sum of all edges  =  4[ l + w + h ] = 17 →  l + w + h = 17/4     square both sides

 

l^2 + w^2 + h^2  + 2 ( lw + lh + wh) = 289/16       (1) 

 

Surface area  =   2 [ lw + lh + wh ] =  15     (2)

 

Sub (2)  into (1)

 

l^2 + w^2 +  h^2  +   15 =  289/16

 

l^2 + w^2 + h^2  =  49/16

 

The length of the diagonal  = 

 

sqrt [ l^2 + w^2 + h^2 ]  =  sqrt [ 49/16 ]   = 7 / 4  =   1.75

 

 

cool cool cool

 May 30, 2024

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