Ajit has red, yellow, green, and blue tiles. All tiles of the same
colour have the same dimensions. The red and yellow tiles are squares,
and the green and blue tiles are rectangles. Ajit arranges his tiles
into the following rectangle so that none of the tiles are
overlapping.
A larger rectangle is made up of three red squares, two yellow squares, three green rectangles, and one blue rectangle.
The longer side of the large rectangle is formed by the longer side of a green rectangle, the side of a red square, and the longer side of another green rectangle.
The shorter side of the large rectangle is formed by the shorter side of a green rectangle, the side of a yellow square, and the shorter side of another green rectangle.
The length of a yellow square is twice the length of a red square and is the same as the length of the
longer side of a green rectangle.
The length of a red square, the length of the shorter side of a
green rectangle, and the length of the shorter side of a blue rectangle
are all the same.
The length of the longer side of a blue rectangle is the same as
the length of a red square plus the length of a yellow square.
If Ajit wanted to use only red squares to make a rectangle with the
same dimensions, how many red squares would he need?
