A rectangular piece of cardboard, whose area is 396 square centimeters, is made

Question

A rectangular piece of cardboard, whose area is 396 square centimeters, is made into an open box by cutting a 2 centimeter
square from each corner and turning up the sides. If the box is to have a volume of 504 cubic centimeters, what size cardboard should you start with? A rectangular piece of cardboard, whose area is 396 square centimeters, is made into an open box by cutting a 2 centimeter
square from each corner and turning up the sides. If the box is to have a volume of 504 cubic centimeters, what size cardboard should you start with?

Explanation / Answer

let the length and width of cardboard be x and y respectively

area is 396 square centimeters

x*y =396

=>y=396/x

length of box =x-(2*2) =x-4

width of box =y-(2*2) =y-4

height of box =2

volume of box is 504 cubic centimeters

=>(x-4)*(y-4)*2=504

=>xy-4x-4y+16=252

=>396-4x-4(396/x)+16=252

=>4x+4(396/x)=160

=>x+(396/x)=40

=>x2-40x+396=0

=>x=18 , x=22

y=396/x,x=18

=>y=396/18

=>y=22

y=396/x,x=22

=>y=396/22

=>y=18

so size of cardboard should be 22 cm x 18cm or  18 cm x 22cm

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