Mathematics
Grey Kangaroo
2022
19

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

Answer

D

SOLUTIOn

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 4X + 4Y + 2Z = 72, 4X + 2Y + 4Z = 96 and 2X + 4Y + 4Z = 102. When you add these three equations together you obtain 10X + 10Y + 10Z = 270 and hence the surface area of the brick is 2X + 2Y + 2Z = 270 ÷ 5 = 54.

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