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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.

 Mar 25, 2024
 #1
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15  =  2 ( WL + LH + WH)

 

17 =  4 (W + L + H)

4.25 = W + L + H        square both sides

18.0625 =  H^2 + 2 H L + 2 H W + L^2 + 2 L W + W^2

 

18.0625  =  2 [ WL + LH + WH]  +  W^2 + L ^2  + H^2

18.0625 =  15  + W^2 + L^2 + H^2

3.0625  =  W^2 + L^2 + H^2

 

Length of diagonal  =  sqrt [ W^2 + L^2 + H^2 ] =  sqrt [ 3.0625 ]  =  1.75

 

 

cool cool cool

 Mar 26, 2024

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