The Lee family wants to buy a new round dining table. Their rectangular door frame is 3 feet wide and 6.5 feet high. If the legs are attached to the table, approximate the greatest length of its diameter so that the table can be placed into the dining room.
There's a lot of possible data missing, but if the statement about having the legs attached is supposed to mean that the table must be carried straight through the door, legs first, then the diameter cannot be greater than the width of the door: 3 feet.
To determine the greatest length of the diameter that can fit through the door frame, we need to consider the diagonal length of the table. We can use the Pythagorean theorem to calculate it.
1. Start by squaring the width and height of the door frame separately:
- Width squared: 3 feet x 3 feet = 9 square feet
- Height squared: 6.5 feet x 6.5 feet = 42.25 square feet
2. Add the two squared values together:
- 9 square feet + 42.25 square feet = 51.25 square feet
3. Take the square root of the sum to find the diagonal length:
- Square root of 51.25 = 7.16 feet (approximately)
So, the greatest length of the diameter of the round dining table that can fit through the door frame is approximately 7.16 feet.
To find the greatest length of the diameter of the round dining table that can fit through the door frame, we need to ensure that the table can be maneuvered at an angle through the door. Here's how you can approach this problem:
1. Determine the maximum diagonal length of the door frame: The maximum diagonal length is the square root of the sum of the squares of the width and height of the door frame. In this case, it would be √(3^2 + 6.5^2) = √(9 + 42.25) = √51.25 ≈ 7.16 feet.
2. The greatest length of the diameter should be smaller than the maximum diagonal length of the door frame. To ensure that the table can fit through the door at an angle, subtract a small clearance value from the maximum diagonal length. Let's assume a clearance of 1 foot.
3. Subtract the clearance value from the maximum diagonal length: 7.16 feet - 1 foot = 6.16 feet.
Therefore, the greatest length of the diameter for the round dining table should be approximately 6.16 feet in order for it to fit through the door frame, accounting for a clearance of 1 foot.