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.

Result

a =  84 cm
b =  62 cm

Solution:

a=22+b 6 a26 b2=19272  6 a26 (a22)2=19272 264a=22176 a=22176/264=84  a=84=84  cm 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 / 264 = 84 \ \\ \ \\ a = 84 = 84 \ \text { cm }
b=a22=8422=62=62  cm b = a-22 = 84-22 = 62 = 62 \ \text { cm }



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