A rectangular prism has a total surface area of $36.$ Also, the sum of all the edges of the prism is $32.$ Find the length of the diagonal joining one corner of the prism to the opposite corner.
x * y * 4 + y * y * 2 = 36 x = long side y = short side length
4x + 8 y = 32 y = 4 -.5 x
x *(4-.5x) * 4 + (4-.5x)^2 * 2 = 36 expand then simplify, then
Quadratic Formula x = 4.77485 then y = 1.613 diagonal is then sqrt ( 1.613^2 + 1.613^2 + 4.775^2) = sqrt (24 ) = 5.29
