+136 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.
+129647 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
