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

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