15. The diameter of the circle shown is $10 \mathrm{~cm}$. The circle passes through the vertices of a large rectangle which is divided into 16 identical smaller rectangles.
What is the perimeter of the shape drawn with a dark line?
A $10 \mathrm{~cm}$
B $16 \mathrm{~cm}$
C $20 \mathrm{~cm}$
D $24 \mathrm{~cm}$
E $30 \mathrm{~cm}$
rectangle has length $2.5 \mathrm{~cm}$. The perimeter of the marked shape is made up of eight diagonals of the small rectangles and hence has length $8 \times 2.5 \mathrm{~cm}=20 \mathrm{~cm}$.
15. C The diagonals of a rectangle bisect each other at the midpoint of the rectangle. Hence, the midpoint of a rectangle is equidistant from all four vertices and is the centre of a circle through its vertices.
In this case, the diameter of the circle is $10 \mathrm{~cm}$. This is equal to the sum of the lengths of the diagonals of four of the smaller rectangles. Hence the diagonal of each small