Final answer:
To find a square that remains a square if it is increased or decreased by 5, we can find a side length 'x' for which (x + 5)^2 and (x - 5)^2 are perfect squares. For example, a square with a side length of 20 satisfies the given conditions.
Step-by-step explanation:
To find a square that remains a square if it is increased or decreased by 5, we need to consider the relationship between the side length of the original square and the side length of the new square. Let's assume the original square has a side length of 'x'. If we increase the side length by 5, the new square will have a side length of 'x + 5', and if we decrease the side length by 5, the new square will have a side length of 'x - 5'.
To find a square that remains a square, we need to find 'x' such that 'x + 5' and 'x - 5' are also perfect squares. This means that we need to find a number 'x' for which (x + 5)^2 and (x - 5)^2 are perfect squares.
For example, let's take 'x = 20'. In this case, the new square with a side length of '20 + 5 = 25' is still a perfect square (5^2 = 25), and the new square with a side length of '20 - 5 = 15' is also a perfect square (3^2 = 9).
Therefore, a square with a side length of 20 satisfies the given conditions.