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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.

 Jun 25, 2024
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Surface area =

2(LW + WH + LH) = 15

 

Sum of edges  =  4 (L + W + H)  = 17  →  L + W + H = 17/4....square both sides

 

L^2 + W^2 + H^2 + 2 (LW + WH + LH)  =  289 / 16

 

L^2 + W^2 + H^2 +  15 = 289/16

 

L^2 + W^2 + H^2  =  289/16 - 15  =  49/16

 

Length of diagonal  = sqrt [ L^2 + W^2 + H^2 ] = sqrt [ 49 / 16 ]  =  7 / 4  =  1.75

 

cool cool cool

 Jun 25, 2024

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