A metal door can expand by up to 0.3% of its height and width in hot summer temperatures. If the door expands to more than the height or width of the door frame, it will not open or close property.
Wanda wants to install a metal door in a door frame that is 2.1 meters tall and 0,9 meters wide.
Which door will BEST fit the door frame and still open and close properly in the summertime?
Q a door that measures 2.093 by 0.897 meters, measured to the nearest millimeter
a door that measures 2.09 by 0.89 meters, measured to the nearest centimeter
• a door that measures 2.090 by 0.890 meters, measured to the nearest millimeter
• a door that measures 2.08 by 0.88 meters, measured to the nearest centimeter
To determine which door will best fit the door frame and still open and close properly in the summertime, we need to take into account the expansion of the metal door.
The door frame is 2.1 meters tall and 0.9 meters wide. If the metal door expands by up to 0.3% of its height and width, we can calculate the maximum allowable expansion for the door.
For the height: 0.3% of 2.1 meters = 0.0063 meters = 6.3 millimeters.
For the width: 0.3% of 0.9 meters = 0.0027 meters = 2.7 millimeters.
Based on this calculation, the door should not expand more than 6.3 millimeters in height and 2.7 millimeters in width to still open and close properly.
Now let's compare the dimensions of the doors listed:
1. The door measuring 2.093 by 0.897 meters is larger than the allowable expansion, so it will not open or close properly.
2. The door measuring 2.09 by 0.89 meters is larger than the allowable expansion, so it will not open or close properly.
3. The door measuring 2.090 by 0.890 meters is within the allowable expansion, so it should open and close properly.
4. The door measuring 2.08 by 0.88 meters is smaller than the allowable expansion, so it may open and close properly, but there will be extra space around the edges.
Therefore, the door that will best fit the door frame and still open and close properly in the summertime is the one that measures 2.090 by 0.890 meters, measured to the nearest millimeter.
To determine which door will best fit the door frame and still open and close properly in the summertime, we need to consider the expansion of the metal door.
Given that the metal door can expand by up to 0.3% of its height and width, we can calculate the maximum expansion for both the height and width of the door frame.
For the height:
0.3% of 2.1 meters = (0.3/100) * 2.1 = 0.0063 meters
For the width:
0.3% of 0.9 meters = (0.3/100) * 0.9 = 0.0027 meters
Now, let's compare these expansion values with the measurements of each door option:
Door Option 1: 2.093 by 0.897 meters
Height expansion: 2.093 - 2.1 = -0.007 meters
Width expansion: 0.897 - 0.9 = -0.003 meters
Door Option 2: 2.09 by 0.89 meters
Height expansion: 2.09 - 2.1 = -0.01 meters
Width expansion: 0.89 - 0.9 = -0.01 meters
Door Option 3: 2.090 by 0.890 meters
Height expansion: 2.090 - 2.1 = -0.01 meters
Width expansion: 0.890 - 0.9 = -0.01 meters
Door Option 4: 2.08 by 0.88 meters
Height expansion: 2.08 - 2.1 = -0.02 meters
Width expansion: 0.88 - 0.9 = -0.02 meters
Based on the calculations, Option 1 has the closest measurements to the door frame dimensions. However, it has negative values for both height and width expansion, indicating that it will not fit properly in the door frame when the metal door expands.
Therefore, the option that will best fit the door frame and still open and close properly in the summertime is Option 3, which measures 2.090 by 0.890 meters, measured to the nearest millimeter. Although it has slightly negative values for expansion, they are closer to zero compared to the other options and are within an acceptable range for the door to function properly.
To determine which door will best fit the door frame and still open and close properly in the summertime, we need to consider the expansion of the metal door in hot temperatures.
The metal door can expand by up to 0.3% of its height and width.
For the door frame with a height of 2.1 meters:
- 0.3% of 2.1 meters = (0.3/100) * 2.1 meters = 0.0063 meters
For the door frame with a width of 0.9 meters:
- 0.3% of 0.9 meters = (0.3/100) * 0.9 meters = 0.0027 meters
Now let's compare the expansion of the door frame to the measurements of the doors provided:
1. Door measuring 2.093 by 0.897 meters (measured to the nearest millimeter):
- The expansion of the door frame height is 0.0063 meters, and the door height is 2.093 meters, which is greater than the expansion. So, the door will not fit properly in terms of height.
- The expansion of the door frame width is 0.0027 meters, and the door width is 0.897 meters, which is greater than the expansion. So, the door will not fit properly in terms of width.
2. Door measuring 2.09 by 0.89 meters (measured to the nearest centimeter):
- The expansion of the door frame height is 0.0063 meters, and the door height is 2.09 meters, which is greater than the expansion. So, the door will not fit properly in terms of height.
- The expansion of the door frame width is 0.0027 meters, and the door width is 0.89 meters, which is greater than the expansion. So, the door will not fit properly in terms of width.
3. Door measuring 2.090 by 0.890 meters (measured to the nearest millimeter):
- The expansion of the door frame height is 0.0063 meters, and the door height is 2.090 meters, which is equal to the expansion. So, the door will fit properly in terms of height.
- The expansion of the door frame width is 0.0027 meters, and the door width is 0.890 meters, which is equal to the expansion. So, the door will fit properly in terms of width.
4. Door measuring 2.08 by 0.88 meters (measured to the nearest centimeter):
- The expansion of the door frame height is 0.0063 meters, and the door height is 2.08 meters, which is less than the expansion. So, the door will fit properly in terms of height.
- The expansion of the door frame width is 0.0027 meters, and the door width is 0.88 meters, which is less than the expansion. So, the door will fit properly in terms of width.
Based on these comparisons, the door that will BEST fit the door frame and still open and close properly in the summertime is the door measuring 2.090 by 0.890 meters, measured to the nearest millimeter.