Question

Matt looks at the architectural plan of a four-walled room 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 20.2 inches. Is the room in the shape of a square? Explain how you determined your answer. Show all your work.

A) Yes, because the diagonal is longer than any of the walls.
B) No, because the diagonal is shorter than any of the walls.
C) Yes, because the diagonal is equal to the sum of the two shorter walls.
D) No, because there is not enough information to determine the shape.

Answer 1

The room cannot be determined as a square because we only have one side's length and the diagonal, and given these values, they do not satisfy the conditions of a square room. Correct answer is D) No, because there is not enough information to determine the shape.

Step-by-step explanation:

To determine if a room is square, we need to see if all sides are of equal length. Since we have a diagonal measurement and only one side length, we can use the Pythagorean theorem to test for a square room. A square room would have the property that the diagonal (d) is equal to the square root of the sum of the squares of the sides (a and b). If the room is square, both sides should have the same length (a=b), so we can represent this as d^2 = a^2 + a^2 = 2a^2. Given the diagonal, d = 20.2 inches, and one side, a = 19 inches, we can square these to get d^2 = 20.2^2 = 408.04 and a^2 = 19^2 = 361. If the room was square, we'd expect 2a^2 to be equal to d^2. So, 2 * 361 = 722 which is not equal to 408.04. That tells us that the room is not a square.

Therefore, the correct answer is D) No, because there is not enough information to determine the shape. We cannot conclusively say it's a square as we only know one side's length and the length of the diagonal; however, with the given numbers, they do not satisfy the condition of a square.