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.

Question

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

GPT 3.5 · Answer

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.