# What is the ratio of dimensions of this special rectangle ?

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What should be the ratio of the dimensions of a rectangle such that when you take off of it a largest possible square you end up with a rectangle with the same aspect ratio as that of the original ?

posted Apr 6, 2017

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This involves solving for the Golden Ratio which is .618:1.
Thus the rectangle would be 1 unit long by .618 units in height. And of course the square would be .618 x .618.

See calculations below, for solving the ratio of the Golden Section which is transformed into a quadratic equation which is then solved by the quadratic formula:

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What are the dimensions of rectangle A6 in the following image?

Assumptions
1. A sheet of A0 paper is a rectangle with an area of precisely one square meter. Its length (the long side) is twice its width.
2. When A0 paper is cut in half across its long side, two sheets of A1 paper are formed. Likewise, when A1 paper is cut in half across its long side, A2 paper is formed, and so on.
3. All rectangles in the series (A0, A1, A2, ...) are similar.