19. A builder has two identical bricks. She places them side by side in three different ways, as shown. The surface areas of the three shapes obtained are 72,96 and 102 . What is the surface area of the original brick?
A 36
B 48
C 52
D 54
E 60
Solution
D

Let the areas of the front, the side and the top of the bricks be $X, Y$ and $Z$, as shown in the diagram. From the question, we see that $4 X+4 Y+2 Z=72,4 X+2 Y+4 Z=96$ and $2 X+4 Y+4 Z=$ 102. When you add these three equations together you obtain $10 X+10 Y+10 Z=270$ and hence the surface area of the brick is $2 X+2 Y+2 Z=270 \div 5=54$