Matt looked at the architectural plan of a room with four walls in which the walls meet each other at right angles. the length of one wall in the plan is 19 inches. the length of the diagonal of the floor of the room in the plan is approximately 20.62 inches. is the room in the shape of a square? explain how you determined your answer. show all your work.

To quickly calculate this problem, we multiply the square root of two to 19 inches and check if the product is equal to 20.62 inches. Square root of two comes from the pythagorean theorem assuming the angle of the corners is 90 degrees. In this case, the answer is 26.87 inches which is greater than 20.62 inches. This means the shape of the room is not a square.