Explanation:
a box without top has 5 rectangular sides :
bottom
left and right
front and back
the surface area is the sum of the individual rectangle areas.
height = 6×length
length = height/6
height = width
bottom = length × width
left and right = 2× width × height
front and back = 2× length × height
we are bringing all to expressions of height :
bottom = height/6 × height = height²/6
left and right = 2× height × height = 2×height²
front and back = 2× height/6 × height = height²/3
the sum of all that is
height²/6 + 2×height² + height²/3 = 576
bringing all to .../6 :
height²/6 + 12×height²/6 + 2×height²/6 = 576
15×height²/6 = 576
5×height²/2 = 576
5×height² = 1152
height² = 1152/5 = 230.4
height = sqrt(230.4) = 15.17893277... cm
length = height/6 = 2.529822128... cm
width = height = 15.17893277... cm