+357 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.
+128578 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
