Two cubes

The surfaces of two cubes, one of which has an edge of 22 cm longer than the second are differ by 19272 cm². Calculate the edge length of both cubes.

Correct answer:

a =  84 cm
b =  62 cm

Step-by-step explanation:

$$\begin{gathered} a=22+b \\ 6\cdot a^2-6\cdot b^2=19272 \\ 6\cdot a^2-6\cdot (a-22{)}^2=19272 \\ 264a=22176 \\ a=22176\mathrm{/}264=84 \\ a=84\text{ cm} \end{gathered}$$

$b=a-22=84-22=62\text{ cm}$

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