Final answer:
The room is not a square since the floor diagonal length of 20.62 inches does not match the expected diagonal length of a square room with 19-inch sides, which should be approximately 26.87 inches according to the Pythagorean theorem.
Step-by-step explanation:
To determine if the room is a square, we need to consider the properties of a square. A square has four equal-length sides and right angles at each corner. According to the Pythagorean theorem, for a square with sides of length s, the diagonal d would be calculated as d = s√2.
Given that one wall is 19 inches, the diagonal for a square room should be 19√2 inches. Calculating this gives a diagonal of approximately 26.87 inches. Since the floor diagonal provided is 20.62 inches, which is shorter than the expected diagonal of a square with 19-inch sides, we can conclude that the room is not a square.