How can I physically generate a square with two 4x4 squares, three 3x3 squares, four 2x2 squares and 4 1x1 squares?
"George has two 4x4 squares, three 3x3 squares, four 2x2 squares, and four 1x1 squares. Draw a diagram to show how she could place some or all of these squares together without gaps or overlaps to make a square that is a big as possible." (From Math Quest 11)
Please provide a visual diagram.
"George has two 4x4 squares, three 3x3 squares, four 2x2 squares, and four 1x1 squares. Draw a diagram to show how she could place some or all of these squares together without gaps or overlaps to make a square that is a big as possible." (From Math Quest 11)
Please provide a visual diagram.
2 Answers
Make a square with an area of
Explanation:
If you work out the total area of all the squares, we have:
TOTAL =
The biggest square that can be made is one with an area of
Note the use of the phrase, "....how she could place all or some of them"... meaning you can have some squares left over.
At this stage there is a bit of trial and error in fitting all the squares together. Start by placing the two biggest squares (
I am not able to give a drawing, but with these hints to get you started, I am sure you will manage.
The maximum possible size is
Explanation:
Though the given squares are large enough to cover a total area of
The largest possible square is
