Final answer:
The statement about the largest rectangle inscribed in a right triangle is true, as it must touch all three sides. The Pythagorean theorem can be applied to such triangles to determine relationships between their sides.
Step-by-step explanation:
The statement that the largest rectangle inscribed in a right triangle touches all three sides of the triangle is true. This is because, for a rectangle to be inscribed in a right triangle, two of its sides must be aligned with the two legs of the right triangle, and the rectangle's corners must touch the hypotenuse. Thus, there is a point of contact on each side of the triangle. When calculating the area or dimensions of such a rectangle or the triangle itself, we can use the Pythagorean theorem if needed. The theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). Mathematically, it is represented as a² + b² = c².