+48 In a rectangular prism, the surface area is 24 and the sum of the lengths of all twelve edges is 24. What is the volume of the prism?
+130536 surface area = 2 (LW + LH + WH) = 24 ⇒ LW + LH + WH = 12
sum of edge lengths = 4 [ L + W + H) = 24 ⇒ L + W + H = 6
Using a little logic and assuming integer values for each dimensinon, each edge measures 2
Proof
L + W + H = 6 LW + LH + WH =12
2 + 2 + 2 = 6 2*2 + 2*2 + 2*2 = 12
The volume = LWH = 2*2*2 = 8 cubic units
