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 fit the door frame and still open and close properly in the summertime, we need to calculate the maximum expansion allowed for both the height and width.
For the height:
0.3% of 2.1 meters = 0.0063 meters
For the width:
0.3% of 0.9 meters = 0.0027 meters
Now, let's compare these measurements to the options given:
a) Door measuring 2.093 meters by 0.897 meters:
Height difference = 2.093 - 2.1 = -0.007 meters (door too small to fit)
Width difference = 0.897 - 0.9 = -0.003 meters (door too small to fit)
b) Door measuring 2.09 meters by 0.89 meters:
Height difference = 2.09 - 2.1 = -0.01 meters (door too small to fit)
Width difference = 0.89 - 0.9 = -0.01 meters (door too small to fit)
c) Door measuring 2.090 meters by 0.890 meters:
Height difference = 2.090 - 2.1 = -0.01 meters (door too small to fit)
Width difference = 0.890 - 0.9 = -0.01 meters (door too small to fit)
d) Door measuring 2.08 meters by 0.88 meters:
Height difference = 2.08 - 2.1 = -0.02 meters (door too small to fit)
Width difference = 0.88 - 0.9 = -0.02 meters (door too small to fit)
None of the given options will fit the door frame properly in the summertime.
To determine the door that will best fit the door frame and still open and close properly in the summer, we need to calculate the maximum expansion allowed for the metal door.
Step 1: Calculate the maximum allowable expansion:
Height expansion = 2.1 meters * 0.3% = 0.0063 meters
Width expansion = 0.9 meters * 0.3% = 0.0027 meters
Step 2: Determine the door dimensions that will still fit within the expanded door frame:
Height of expanded door frame = 2.1 meters + 0.0063 meters = 2.1063 meters
Width of expanded door frame = 0.9 meters + 0.0027 meters = 0.9027 meters
Now let's compare the door options:
Option 1: a door that measures 2.093 by 0.897 meters, measured to the nearest millimeter
This door is smaller than the expanded door frame and will fit properly.
Option 2: a door that measures 2.09 by 0.89 meters, measured to the nearest centimeter
This door is smaller than the expanded door frame and will fit properly.
Option 3: a door that measures 2.090 by 0.890 meters, measured to the nearest millimeter
This door is the same size as the expanded door frame and will fit properly.
Option 4: a door that measures 2.08 by 0.88 meters, measured to the nearest centimeter
This door is smaller than the expanded door frame and will fit properly.
Based on the given options, the door that will best fit the door frame and still open and close properly in the summer is Option 3, which 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 summer, we need to consider the maximum expansion of the metal door.
Given that the door can expand by up to 0.3% of its height and width, we can calculate the maximum expansion allowed for the door:
Maximum height expansion = 2.1 meters * 0.3% = 0.0063 meters
Maximum width expansion = 0.9 meters * 0.3% = 0.0027 meters
Now let's evaluate each door option:
1. Door that measures 2.093 by 0.897 meters, measured to the nearest millimeter:
- This door's height exceeds the maximum allowed expansion (0.0063 meters), so it will not fit properly in the door frame.
2. Door that measures 2.09 by 0.89 meters, measured to the nearest centimeter:
- This door's height is very close to the maximum allowed expansion but still within the limit.
- The width is smaller than the maximum allowed expansion, which ensures a proper fit.
- Thus, this door is a good option since it meets the size requirements.
3. Door that measures 2.090 by 0.890 meters, measured to the nearest millimeter:
- This door has the same dimensions as the previous option but with more precise measurements.
- Both the height and width are within the maximum allowed expansion, so it will fit properly.
4. Door that measures 2.08 by 0.88 meters, measured to the nearest centimeter:
- This door's height and width are smaller than the maximum allowed expansion.
- While it will fit within the frame, it may not provide an optimal seal.
Based on the calculations, the door that measures 2.090 by 0.890 meters, measured to the nearest millimeter, is the BEST option as it meets the size requirements without exceeding the maximum allowed expansion limit.