Imagine you are suspending a cube from one vertex (corner) and
allowing it to hang freely. Now imagine you are lowering it into
water until it is exactly half submerged. What shape does the
surface of the water make around the cube?
What happens to the perimeter of triangle ABC as the two smaller
circles change size and roll around inside the bigger circle?
Draw a square. A second square of the same size slides around the
first always maintaining contact and keeping the same orientation.
How far does the dot travel?
Correct solutions were received from Chen from The Chinese High
School Singapore, Andrei of School 205 Bucharest, Mary of
Brirchwood High School (whose solutions is used as the basis of the
one below) and Sana, Jenny, Chris and Rosion of Madras College, St.
is a 1/3 the length of the rectangle
w is a1/3 the width of the rectangle
area of the rectangle = 3l
x 3w = 9lw
Area triangle A = Area of triangle C = lw
Area triangle B = Area of triangle D= lw
Therefore area of the parallelogram = 9lw
Therefore ratio of the area of the parallelogram to the area of
the rectangle is 5lw