The dimensions of the box are ;
length = 0.82 cm
width = 0.82 cm
height = 5.82 cm
The volume of prism is generally expressed as
volume = base area × height
let the base width be x
the height of the box = x +5
A square has equal sides, therefore
volume = x × x ( x + 5)
4 = x³ + 5x²
= x³ + 5x² - 4 = 0
= (x +1) ( x² + 4x -4) = 0
(x² + 4x -4) = 0
-b ± √b² - 4ac)/2a
x = -4 ± √ 4² - 4 × 1 × -4)/2
x = -4 ± √16+16)/2
x = -4 ± 4√2)/2
x = (-4 + 4√2)/2or (-4 - 4√2)
x = -2 + 2.82) or -2 - 2.82)
x = 0.82 or - 4.82
Therefore the positive value of x is 0.82
= 0.82
therefore x = 0.82
the height = 5 + 0.82 = 5.82cm
Therefore the dimensions of the box could be
length = 0.82 cm
width = 0.82 cm
height = 5.82 cm