Every square number can be written as the sum of two triangular numbers. For example, 16 = 6 + 10. This can be represented geometrically by dividing a square array of dots with a line as shown.
The triangular arrangement above the line represents 6, the one below the line represents 10, and the whole arrangement represents 16. Show how the square numbers 25 and 36 may likewise be geometrically represented as the sum of two triangular numbers.
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