+233 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.
+129630 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
