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Friday, February 12, 2010

3D diagonal

What is the length of the diagonal of a 3D rectangular prism (a cuboid) whose surface area is 94, if the sum of the lengths of the sides is 48?

Labels: mathschallenge

7 Comments:

Chris said...: Wiz. You may be interested in some of my rambling's at Prove that....; February 12, 2010 1:40 PM
Ragknot said...: This post has been removed by the author.; February 12, 2010 4:28 PM
Ragknot said...: I found an error in my code

5 4 3

7.07106781186548; February 12, 2010 4:49 PM
Ragknot said...: ' 5 4 3
' 7.07106781186548
Sub prism()
'3D diagonal
'What is the length of the diagonal of a
'3D rectangular prism (a cuboid) whose
'surface area is 94, if the sum of the
'lengths of the sides is 48?
For L = 1 To 10
For w = 1 To 10
For h = 1 To 10
suml = (4 * L) + (4 * h) + (4 * w)
surf = ((L * w) + (w * h) + (L * h)) * 2
If suml = 48 And surf = 94 Then
a = Sqr(L ^ 2 + w ^ 2)
d = Sqr(a ^ 2 + h ^ 2)
Debug.Print L; w; h; d
End If
Next h
Next w
Next L
End Sub; February 12, 2010 4:52 PM
Anonymous said...: P=4l+4w+4h
SA=2lw+2wh+2lh
d^2=w^2+h^2+l^2

P/4=l+w+h
(P/4)^2=(l+w+h)^2=(l+w+h)(l+w+h)=l^2+lw+lh+wl+w^2+wh+hl+hw+h^2
(P/4)^2=l^2+w^2+h^2+2lw+2wh+2lh
(P/4)^2=d^2+SA
d=sqrt( (P/4)^2-SA)
d=sqrt(12^2-94)
d=sqrt(50)

Answer
d=sqrt(50)

Cam; February 12, 2010 5:13 PM
Chris said...: That'll teach me, I should have tweaked it for all the numbers to be irrational. Off the top of my head, I'm not sure how I would code in that case.

Two correct solutions. And yes it, was 3,4,5 for the sides.; February 12, 2010 5:34 PM
Wizard of O said...: Hi Chris,
I had a look at your later posts in Prove That . . . There's some heavy stuff there. I'll need a bit more time to digest this. I'll get back to you . . .; February 12, 2010 9:54 PM