A rectangular prism has a total surface area of 56. Also, the sum of all the edges of the prism is 60. Find the length of the diagonal joining one corner of the prism to the opposite corner.
+36916 Kinda messy, but here is my solution
w = width
s = side
Sum of edges = 4 w + 8 s = 60
w + 2s = 15
w = 15 - 2s
Surface area = s*s + s*s + w*s + w*s + w*s + w*s = 2s^2 + 4 ws = 56
s^2 + 2ws = 28 sub in the red equation for w
s^2 +2s (15-2s) = 28
s^2 + 30s - 4s^2 - 28 = 0
-3s^2 + 30s-28 = 0 Quadratic formula show s = 1.04189 or 8.95811 (throw out ....too big)
then w = 15-2s = 12.91622
Now we have the dimensions of the 3-d solid diagonal = sqrt ( s^2 + s^2 + w^2) =~~ 13 units
