We are asked whether any three squares could form the sides of a right triangle. Let's try to form a right triangle using the sides of three identical squares with side length a.
Notice that the squares form an equilateral triangle. The measure of each angle in an equilateral triangle is 60^(∘), so this triangle is not a right triangle.
This means that it is not true that any three squares will form the sides of a right triangle. In general, given three squares, we can use the Pythagorean Theorem to justify whether they will form a right triangle. Let's consider three example squares where a, b, and c are the side lengths of the squares.
If the sides of the squares form the sides of a right triangle, then their lengths must satisfy the Pythagorean Theorem. This means that the sum of squares of the side lengths of the two smaller squares a and b must be equal to the square of the side length of the biggest square c.
a^2 + b^2 = c^2
If that is not the case, then the triangle formed by the sides of the squares cannot be a right triangle.
