PSLE
Valen wanted to build a set of steps with 1-cm cubes. The figures show how he built the steps from a height of 2 cm to 3 cm to 4 cm. If Valen continued building the steps in this way, what would be the height of the set of steps that had 90 cubes? Express your answer in cm.
Cubes needed for 2-cm steps = 2 x 3 = 2 x (1 + 2) = 6 cubes
Cubes needed for 3-cm steps = 2 x 6 = 2 x (1 + 2 + 3) = 12 cubes
Cubes needed for 4-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) = 90
9 x 10 = 90

Number of cubes needed for the height of the set of steps that had 90 cubes = 9 

Height of the set of steps that had 90 cubes
= 9 x 1 
= 9 cm

Answer(s): 9 cm