Question

a shipping container must have a volume of 200 m3. the client tells the manufacturer that because of the contents, the length of the container must be 6 m longer than the width and the heigth must be 1 m longer than its width. what should be the dimensions of the container?

Answer 1

l= w+6m

h= w+1m

Vol³= l.b.h

200m³= (w+6)m(w)m(w+1)m

200m³= (w²+6w)(w+1)m³

200= w³+6w²+w²+6w

200= w³+7w²+6w

w³+7w²+6w-200=0

By trial

when w= 4

64+112+24-200=0

Therefore, w-4 is the factor

Note: this step is optional as we already found w

w-4| w³+7w²+6w-200 | w²+11w+50

w³-4w²

11w²+6w

11w²-44w

50w-200

50w-200

(w-4)(w²+11w+50)= 0

so w= 4

l= w+6= 4+6= 10m

h= w+1= 4+1= 5m