The length of a box is 2 centimeters less than its height. the width of the box is 7 centimeters more than its height. If the box had has a volume of 180 cubic centimeters, what is its surface area?

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Answer 1 · 2018-06-17T12:15:51

Let the height of the box be #h# cm
Then its Length will be #(h-2)# cm and its width will be #(h+7)# cm
So by the condtion of the problem

#(h-2)xx(h+7)xxh=180#

#=>(h^2-2h)xx(h+7)=180#

#=>h^3-2h^2+7h^2-14h-180=0#

#=>h^3+5h^2-14h-180=0#

For #h=5# LHS becomes zero
Hence #(h-5)# is factor of LHS

So
#h^3-5h^2+10h^2-50h+36h-180=0#
#=>h^2(h-5)+10h(h-5)+36(h-5)=0#

#=>(h-5)(h^2+10h+36)=0#

So Height #h=5# cm

Now Length #=(5-2)=3# cm

Width #=5+7=12# cm

So the surface area becomes

#2(3xx12+12xx5+3xx5)=222cm^2#