All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars
 perplexus dot info

 Integer Triangle Side Puzzle (Posted on 2015-07-26)
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 No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)
 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

Please log in:
 Login: Password: Remember me: Sign up! | Forgot password

 Search: Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (2)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:
Copyright © 2002 - 2018 by Animus Pactum Consulting. All rights reserved. Privacy Information