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Integer Triangle Side Puzzle (Posted on 2015-07-26) Difficulty: 3 of 5
PQR is a triangle with PQ = 33, PR= 21 and QR = X, where X is an integer.
There are points S and T on the sides PQ and PR respectively such that PS=ST=TR = Y, where Y is an integer.
Find X.

No Solution Yet Submitted by K Sengupta    
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Solution computer solution Comment 1 of 1
The program finds length of ST for all possible combinations of X and Y (used in determining PS and TR). If it equals Y, it's the solution.

DefDbl A-Z
Dim crlf$


Private Sub Form_Load()
 Form1.Visible = True
 
 Text1.Text = ""
 crlf = Chr$(13) + Chr$(10)

 For x = 13 To 53
  cosp = (33 * 33 + 21 * 21 - x * x) / (2 * 33 * 21)
  For y = 1 To 20
    st = Sqr(y * y + (21 - y) * (21 - y) - 2 * y * (21 - y) * cosp)
    diff = Abs(st - y)
    If diff / y < 0.000001 Then
      Text1.Text = Text1.Text & x & Str(y) & Str(cosp) & crlf
    End If
  Next
 Next x
 
 
 Text1.Text = Text1.Text & crlf & " done"
  
End Sub

finds

X = 30; Y = 11; cos(P) ~= .454545454545455

The angle P = acos(45/99) is about 62.9643082105877°.

Edited on July 26, 2015, 11:01 am
  Posted by Charlie on 2015-07-26 10:56:57

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