Final answer:
The largest square that can completely tile a rectangular measuring 14cm by 25cm is 1 cm². This is found by determining the greatest common divisor of the lengths of the sides of the rectangle.
Step-by-step explanation:
The largest square that can completely tile a rectangular measuring 14 centimeters by 25 centimeters is the square with the length of the side equal to the greatest common divisor of the lengths of the sides of the rectangle.
In this case, the greatest common divisor of 14 and 25 is 1. Therefore, the largest square that can tile the given rectangle is 1 cm². This is because a 1 cm by 1 cm square can completely fill up the entire rectangle without leaving any leftover space.
It's important to understand that selecting a square with a larger area may not fit perfectly inside the rectangle, leaving uncovered spaces. Hence, our aim is to find the largest square (in terms of side length) which can fit into the rectangle perfectly.
Learn more about Tiling a Rectangle