Question

A rectangular piece of​ cardboard, whose area is 352 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 432 cubic​ centimeters, what size cardboard should you start​ with?

Answer 1

Dimension of cardboard is 22 m by 16 m

Step-by-step explanation:

Given that,

Area = 352 cm²

Side of each square cutting from corner = 2 cm

Volume of box = 432 cm³

Let the two sides are x and y.

The area of the rectangular piece is

`xy=352`

`y=(352)/(x)` -------- (1)

The volume of the rectangular piece

`2(x-4)((352)/(x)-4)=432`

`x^2-38x+352=0`

`(x-16)(x-22)=0`

x=16,22

Put the value of x in the equation (I)

For x = 16

`y=(352)/(16)=22`

For x = 22

`y=(352)/(22)=16`

Dimension of cardboard is 22 m by 16 m