College algebra

Question

An open box is formed from a rectangular piece of cardboard whose length is 8cm more than its width by cutting squares of 2cm from each corner and folding. If the volume = 256 what are the dimensionS?

Answer 1

Hi again Des,

 

The fact that the squares that were cut out are 2 cm by 2cm means the box you create will have a height of 2 cm

 

w = width

 

l = length

 

l = w + 8

 

volume = lwh = 256

 

256 = (w + 8)(w)(2)     divide by 2

 

128 = w² + 8w      get all terms on one side

 

w² + 8w -128 = 0      factor

 

(w + 16)(w - 8) = 0    set each factor equal to 0

 

w = -16 or w = 8            but w can't be negative

 

w = 8

 

l = 16

 

h = 2