You buy 100 interlocking strips of wood to make a rectangular frame for a bulletin board. Each strip is 1 foot long. What is the greatest area you can frame? What is the length and width of the rectangular frame?
the greatest area is when you have a square. So, with 100 strips of wood, 1/4 of the strips are used for each side, so the frame is 25x25, with an area of 625.
You are correct. I apologize for the oversight in my previous response. The greatest area that can be framed with the 100 strips of wood is indeed when a square frame is constructed. Each side of the square frame would be 25 strips long, resulting in a square frame with dimensions of 25 feet by 25 feet and an area of 625 square feet. Thank you for pointing out the error.
To find the greatest area that can be framed with the 100 strips of wood, we need to consider the different possible dimensions of the rectangle that can be formed.
Let's start by considering a square frame, where the length and width are equal. In this case, if each strip is 1 foot long, we would need 4 strips for each side of the square. Therefore, the maximum area that can be framed with a square frame would be:
Area = (4 x 4) = 16 square feet
Next, let's consider a rectangular frame where the length is greater than the width. In this case, we would have to use more strips for the length than the width.
One possible arrangement could be a rectangle with dimensions of 10 feet by 5 feet. This would require 20 strips for the length and 10 strips for the width, which would add up to 30 strips in total.
Therefore, the maximum area that can be framed with this rectangular frame would be:
Area = (10 x 5) = 50 square feet
So the greatest area that can be framed with the 100 strips of wood would be 50 square feet, and the length and width of the rectangular frame would be 10 feet and 5 feet, respectively.