Square to a rectangle

Kevin has moved some tiles to change the shape of his patio from a square to a rectangle. What are the lengths of the sides of the rectangle?
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Kevin had some square patio tiles which he arranged to make a square.

He decided to change it into a rectangle by making one of the sides 3 tiles shorter, and the other side 4 tiles longer.

To make this change, Kevin only needed to buy one extra tile.

What are the lengths of the sides of the rectangle?

This problem is adapted from the World Mathematics Championships