A rectangular is completety filled with dice. Each dice has volume of 2cm³.The length of the box is 5cm grater than its width and its height is 5cm. Suppose the box holds at most 150dice. What are the posibble dimensions of the box

length = 10.64 cm, width = 5.64 cm, and height = 5 cm.

Step-by-step explanation:

Total volume of dice that filled the box = (150 x 2) cm³

                                         = 300 cm³

Let the length, width and height of the box be represented by l, w and h respectively.

So that;

l = (w + 5) cm

w = w

h = 5 cm

volume of the box = length x width x height

                               = (w + 5) x w x 5

                               = (w + 5) x 5w

                               = 5 + 25w

volume of the box = 5 + 25w

Since the box was completely filled by 150 dice, then;

total volume of dice = volume of the box

300 = 5 + 25w

5 + 25w - 300 = 0

Divide through by 5 to have;

+ 5w - 60 = 0

Applying the quadratic expression,

w = (-b ± ) ÷ 2a

where: a = 1, b = 5 and c = -60

(-5 ± ) ÷ 2

(-5 ± ) ÷ 2

(-5 ± 16.28) ÷ 2

(-5 + 16.28) ÷ 2 OR (-5 - 16.28) ÷ 2

5.64 OR -10.64

Thus, w = 5.64 cm

So that, l = (w + 5) = 10.64 cm

The possible dimensions of the box are: length = 10.64 cm, width = 5.64 cm and height = 5 cm.

lo.lll

step-by-step explanation: