Question

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.

A. Yes, the room is a square.
B. No, the room is not a square.
C. Cannot be determined with the given information.
D. The shape of the room is not mentioned.

Answer 1

The room is not a square because the calculated diagonal length for a square with 19-inch sides would be approximately 26.87 inches, which is longer than the given diagonal length of 20.62 inches, indicating the room is rectangular.

Step-by-step explanation:

No, the room is not in the shape of a square. To determine this, we can use the Pythagorean theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. If the room were square, with sides of length 19 inches, then the diagonal (d) would be calculated using d = √(19^2 + 19^2), which equals approximately 26.87 inches. However, the architectural plan shows the diagonal to be approximately 20.62 inches. Therefore, since the diagonal is shorter than what it should be for a square, we can conclude that the room is rectangular, not square.