### Brain Teasers

# Obscure Oblong

A 4 by 4 square is unusual in that it is the only square, with integral (whole number) length sides, for which the area and perimeter are equal in value.

Find the dimensions of the only oblong (non-square rectangle) with integral length sides, such that the area is equal to the perimeter in value.

Find the dimensions of the only oblong (non-square rectangle) with integral length sides, such that the area is equal to the perimeter in value.

### Answer

3 by 6 (area=3x6=18, perimeter=3+6+3+6=18)Hide Answer Show Answer

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## Comments

I'm sorry, but could you say that again in english? I thought an oblong was a musical instrument.

The family of shapes called rectangles contains squares and oblongs. That is, a rectangle that is not a square is called an oblong.

What I liked about this teaser is the word "only". Trying to figure out whether or not there could be another was a challenge. But there isn't another because if x and y are the sides then x=2y/(y-2). When x = 3 y is 6 and when x= 6 y=3. Thereafter as x goes to infinite y is always greater than 2 and less than 3! No more whole number solutions!

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