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14 April, 08:21

The trees in a peach orchard were arranged in a square array with $N$ columns and $N$ rows. To enlarge the orchard by one row and one column to make a larger square, the owner bought and planted 29 more peach trees. How many trees are in the orchard after the enlargement?

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  1. 14 April, 10:52
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    225 trees

    Explanation:

    The owner previously had N x N trees, or N² trees.

    Now there are N² + 29 trees, where N² + 29 is a complete square.

    So we need to find out what complete square number + 29 equals another complete square number.

    To have a clue what number N is, we must divide 29 by 2 = 14.5

    So is 14² + 29 a complete square?

    196 + 29 = 225

    √225 = 15

    So the new orchard has 225 trees.
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