Question
What are the dimensions of a rectangle with a perimeter of 50 feet?
Answers
Answered by
GPT-4o mini
To find the dimensions of a rectangle with a given perimeter, we can use the formula for the perimeter of a rectangle:
\[ P = 2(l + w) \]
where \( P \) is the perimeter, \( l \) is the length, and \( w \) is the width.
Given that the perimeter \( P = 50 \) feet, we can set up the equation:
\[ 50 = 2(l + w) \]
Dividing both sides by 2 gives:
\[ l + w = 25 \]
Now, the length \( l \) and width \( w \) can be any pair of positive numbers that add up to 25. For example:
1. If \( l = 20 \) feet, then \( w = 25 - 20 = 5 \) feet.
2. If \( l = 15 \) feet, then \( w = 25 - 15 = 10 \) feet.
3. If \( l = 12.5 \) feet, then \( w = 25 - 12.5 = 12.5 \) feet.
In conclusion, there is an infinite number of combinations for the dimensions of the rectangle (as long as they are positive), as long as the sum of the length and width is 25 feet.
\[ P = 2(l + w) \]
where \( P \) is the perimeter, \( l \) is the length, and \( w \) is the width.
Given that the perimeter \( P = 50 \) feet, we can set up the equation:
\[ 50 = 2(l + w) \]
Dividing both sides by 2 gives:
\[ l + w = 25 \]
Now, the length \( l \) and width \( w \) can be any pair of positive numbers that add up to 25. For example:
1. If \( l = 20 \) feet, then \( w = 25 - 20 = 5 \) feet.
2. If \( l = 15 \) feet, then \( w = 25 - 15 = 10 \) feet.
3. If \( l = 12.5 \) feet, then \( w = 25 - 12.5 = 12.5 \) feet.
In conclusion, there is an infinite number of combinations for the dimensions of the rectangle (as long as they are positive), as long as the sum of the length and width is 25 feet.