MC)
o inches.
Maria 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 13 inches. The length of the diagonal of the floor of the room in the plan is approximately
Is the room in the shape of a square? Explain how you determined your answer. Show all your work. (10 points)
To determine if the room is in the shape of a square, we need to calculate the length of the diagonal of the floor of the room.
Let's call the length of one wall in the plan "a", which is 13 inches.
In a square, all four walls are equal in length. So, the length of each wall is also "a" inches.
Using the Pythagorean theorem, we can find the length of the diagonal. The Pythagorean theorem states that in a right-angled triangle, the square of the length of the hypotenuse (diagonal in this case) is equal to the sum of the squares of the other two sides.
So, for a square, the diagonal (d) can be calculated as:
d^2 = a^2 + a^2
d^2 = 2a^2 .......(1)
Substituting the value of "a" (13 inches) into equation (1):
d^2 = 2(13^2)
d^2 = 338
Taking the square root of both sides:
d = √338
d ≈ 18.38 inches
Therefore, the length of the diagonal of the floor of the room in the plan is approximately 18.38 inches.
Since the length of the diagonal is different from the length of the walls (13 inches), the room is not in the shape of a square.