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Larger area / larger perimeter (Posted on 2017-07-03) Difficulty: 2 of 5
Find the smallest pair of integer sided rectangles that fit the following criteria:

The first has three times the area of the second and
the second has three times the perimeter of the first.

No Solution Yet Submitted by Jer    
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Solution computer solution | Comment 2 of 3 |

The smallest pair in both senses (area and perimeter) is a 15x22 and a 1x110. The table shows no set is smaller in either consideration.

                     large  first rectangle's
 h  w      h   w     area semi-perimeter
15 22       1 110     330   37
12 35       1 140     420   47
11 48       1 176     528   59
31 42       2 217     1302   73
30 44       2 220     1320   74
26 57       2 247     1482   83
24 70       2 280     1680   94
10 87       1 290     870   97

DefDbl A-Z
Dim crlf$


Private Sub Form_Load()
 Form1.Visible = True
 
 
 Text1.Text = ""
 crlf = Chr$(13) + Chr$(10)
 
 For tot = 1 To 100
   tot2 = 3 * tot
   For a = 1 To tot / 2
     b = tot - a
     For c = 1 To tot2 / 2
        d = tot2 - c
        If a * b = 3 * c * d Then
          Text1.Text = Text1.Text & a & Str(b) & "      " & Str(c) & Str(d)
          Text1.Text = Text1.Text & "     " & a * b & "   " & a + b & crlf
        End If
        DoEvents
     Next
   Next
 Next
 
 Text1.Text = Text1.Text & crlf & " done"
  
End Sub

  Posted by Charlie on 2017-07-03 14:24:05
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