PSLE
Ryan wanted to build a set of steps with 5-cm cubes. The figures show how he built the steps from a height of 10 cm to 15 cm to 20 cm. If Ryan continued building the steps in this way, what would be the height of the set of steps that had 72 cubes? Express your answer in cm.
Cubes needed for 10-cm steps = 2 x 3 = 2 x (1 + 2) = 6 cubes
Cubes needed for 15-cm steps = 2 x 6 = 2 x (1 + 2 + 3) = 12 cubes
Cubes needed for 20-cm steps = 2 x 10 = 2 x (1 + 2 + 3 + 4) = 20 cubes

Formula:
Number of cubes needed for the set of steps
= 2 x (1 + 2 + 3 + ... + Height)
= 2 x ^{(Height) x (Height + 1)}₂ 
= Height x (Height + 1)

Height x (Height + 1) = 72
8 x 9 = 72

Number of cubes needed for the height of the set of steps that had 72 cubes = 8 

Height of the set of steps that had 72 cubes
= 8 x 5 
= 40 cm

Answer(s): 40 cm