A rectangular prism has a total surface area of 56. Also, the sum of all the edges of the prism is \(56\). Find the length of the diagonal joining one corner of the prism to the opposite corner.
+130071 Surface area = 2 ( ab + bc + ac) = 56 (1)
Length of the surface edges = 4 ( a + b + c) = 56
So a + b + c = 14
Square both sides of this
a^2 + 2 ab + 2 ac + b^2 + 2 bc + c^2 = 196 rearrange as
a^2 + b^2 +c^2 + 2 (ab + bc + ac) = 196 (2)
Sub (1) into (2)
a^2 + b^2 + c^2 + 56 = 196
a^2 + b^2 + c^2 = 140
Length of the dagonal = sqrt [ a^2 + b^2 + c^2 ] = sqrt (140) = 2sqrt (35)
