A standard doorway measures 6 feet 8 inches by 3 feet. What is the largest dimension that will fit through the doorway without bending?
You are looking for the diagonal, let it by x
x^2 = (20/3)^2 + 3^2 = 481/9
x =√(481/9) = appr 7.31 ft
or appr 7 feet 3 inches
To determine the largest dimension that will fit through the doorway without bending, we need to compare the dimensions of the doorway to the object we are trying to fit through.
The doorway measures 6 feet 8 inches by 3 feet. Let's convert these dimensions to a common unit of measurement for easier comparison.
1 foot is equal to 12 inches, so 6 feet is equal to 6 * 12 = 72 inches.
Similarly, 3 feet is equal to 3 * 12 = 36 inches.
Therefore, the dimensions of the doorway are 72 inches by 36 inches.
Now, let's compare these dimensions to the object we want to fit through the doorway. We need to make sure that both the height and width of the object are smaller than the corresponding dimensions of the doorway.
If the height of the object is larger than 72 inches, it will not fit through the doorway without bending. Similarly, if the width of the object is larger than 36 inches, it will not fit without bending.
So, the largest dimension that will fit through the doorway without bending is 72 inches for the height and 36 inches for the width.