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Cinq Confusion (Posted on 2014-07-10) Difficulty: 3 of 5
A farmer has two rectangular fields with a peculiar relationship. Both fields have integer dimensions. The corn field has five times the area of the hay field but the hay field has five times the perimeter of the corn field.

It is also known that the dimensions of the corn field differ by 1, and the shorter dimension of the hay field is less than 100.

Find the dimensions of the two fields.

No Solution Yet Submitted by K Sengupta    
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Solution computer solution Comment 2 of 2 |
FOR cornwide = 1 TO 500
    cornlong = cornwide + 1
    cornarea = cornwide * cornlong
    IF cornarea MOD 5 = 0 THEN
        hayarea = cornarea / 5
        cornperio2 = cornwide + cornlong
        hayperio2 = 5 * cornperio2
        FOR haywide = 1 TO hayperio2 / 2
            haylong = hayperio2 - haywide
            IF haywide * haylong = hayarea THEN
                PRINT cornwide; cornlong, haywide; haylong
                PRINT 2 * (cornwide + cornlong); cornwide * cornlong,
                PRINT 2 * (haywide + haylong); haywide * haylong,
                _CLIPBOARD$ = STR$(cornwide) + STR$(cornlong) + "    " + STR$(haywide) + STR$(haylong) + CHR$(13) + CHR$(10)
                _CLIPBOARD$ = _CLIPBOARD$ + STR$(2 * (cornwide + cornlong)) + STR$(cornwide * cornlong)
                _CLIPBOARD$ = _CLIPBOARD$ + STR$(2 * (haywide + haylong)) + STR$(haywide * haylong)
            END IF
        NEXT
    END IF
NEXT

finds
dimensions:
  corn         hay
 249 250     5 2490
perimeter and area:
   corn         hay
 998 62250 4990 12450

Edited clipboard version of perimeter formula to add needed parentheses. Perimeters appeared correct on screen but added to clipboard for pasting here missed the needed parentheses.

Edited on July 10, 2014, 12:47 pm
  Posted by Charlie on 2014-07-10 11:55:08

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