8. The diagram shows two 10 by 14 rectangles which are edge-to-edge and share a common vertex. It also shows the centre $O$ of one rectangle and the midpoint $M$ of one edge of the other.
What is the distance $O M$ ?
A 12
B 15
C 18
D 21
E 24
8. B Let $P$ be a point inside one of the rectangles such that $O P$ is parallel to the horizontal edges of the rectangles and $M P$ is parallel to the vertical edges. Therefore $\angle O P M$ is a right angle.
Then $O P=\frac{1}{2} \times 14+\frac{1}{2} \times 10=7+5=12$.
Also, $M P=14-\frac{1}{2} \times 10=14-5=9$.
By Pythagoras' Theorem, $O M^{2}=O P^{2}+M P^{2}=12^{2}+9^{2}=144+81=225$. Therefore $O M=\sqrt{225}=15$.