Gina 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 17 inches. The length of the diagonal of the floor of the room in the plan is approximately 18.79 inches.
Is the room in the shape of a square? Explain how you determined your answer. Show all your work.
To determine if the room is in the shape of a square, we can first calculate the length of the diagonal of the wall.
Using the Pythagorean theorem, we can find the length of the diagonal (d) using the lengths of the sides (a and b):
d^2 = a^2 + b^2
In this case, we know that one wall has a length of 17 inches. Let's call the other wall length x inches.
d^2 = 17^2 + x^2
d^2 = 289 + x^2
Next, we know the length of the diagonal of the floor is approximately 18.79 inches. Let's call this length y inches.
So, we have the equation:
y^2 = 17^2 + x^2
Now, we can compare the two equations:
d^2 = y^2
289 + x^2 = y^2
Since both equations are equal to the square of the diagonal, we can set them equal to each other:
289 + x^2 = y^2
Substituting in the approximate value for the length of the diagonal of the floor:
289 + x^2 = 18.79^2
Simplifying the equation:
x^2 = 18.79^2 - 289
x^2 = 352.1041 - 289
x^2 = 63.1041
Taking the square root of both sides to isolate x:
x ≈ √63.1041
x ≈ 7.946 inches
Since we found that the length of the other wall is approximately 7.946 inches, and the length of the first wall is 17 inches, the two walls are not equal in length. Therefore, the room is not in the shape of a square.