+2862 A "rectangular" parellelpiped has rectangles for all its faces. The sum of the lengths of the four diagonals of a "rectangular" parrallelpeped is 28. The diagonal of one face has length \(2\sqrt{10}\), while hte diagonal of another face has length \(3\sqrt{5}\). Find the number of cubic units in the volume of the rectangular parellelpiped. (Mathcounts Competitions)
So this is how I think I set up equations
x2 + y2 = 40
y2 + z2 = 45
\((40+z^2)=49\)
Lol third equation took me intense thinking to come up with
The text highlighted in yellow I am confused if it is talking about the diagonals of the entire three dimensional figure, because thats how I set up my equation for. Can someone check if the equation I set up is correct or if I misinterpreted the question?
+6248 \(4\sqrt{x^2+y^2+z^2} = 28\\ x^2 + y^2 + z^2 = 49\\ \text{The other two equations are correct}\)
\(z^2 = 49-40 = 9\\ z=3\\ y^2 = 45-9=36\\ y=6\\ x^2 = 49-36-9 = 4\\ x=2\\ xyz = 36\)
+2862 My last equation is correct too I just substituted in for x^2 + y^2, but thank you though!
