Question 1126992: To comply with FAA regulations, a piece of luggage must be checked to the luggage compartment of the plane if its combined linear measurement of length, width, and height is over 45 in. Katie's suitcase has a total volume of 4200 in.3. Its length is 30 in., and its width is 4 in. greater than the height. Find the dimensions of the suitcase. Will this suitcase need to be checked? Explain.Solve by completing the square.
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! height is x
width is x+4
volume is 30x(x+4)=4200
30x^2+120x-4200=0
divide by 30
x^2+4x-140=0
(x+14)(x-10)=0
x=10 inches height
x+4=14 inches width
the three numbers area 30,10,14, and theyadd to 54. Will need to be checked.
By completing the square
x^2+4x+4=144, moving the 140 across
(x+2)^2=12^2
x+2=+/-12
x=-14 or 10
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