w4st314nd
contestada

!! IMPORTANT !! WILL GIVE BRAINLIEST !!

Lorene plans to make several open-topped boxes in which to carry plants. She makes the boxes from rectangular sheets of cardboard from which she cuts out 10-in squares from each corner. The length of the original piece of cardboard is 20 inches more than the width. If the volume of the box is 1250 in^3, determine the dimensions of the original piece of cardboard.
(figure of the problem is shown in attached picture)
The dimensions of the original piece of cardboard are _ inches by _ inches.

!! PLEASE HELP !! THANKS !!​

IMPORTANT WILL GIVE BRAINLIEST Lorene plans to make several opentopped boxes in which to carry plants She makes the boxes from rectangular sheets of cardboard class=

Respuesta :

Answer:

25 in by 45 in.

Step-by-step explanation:

The length of the box will be x + 20 - 10 - 10 = x

The width of the box will be x - 10 - 10 = x - 20

The height of the box will be 10

So the volume = length x width x height

                        = x(x - 20)10 = 1250

                        =   [tex]10x^{2} - 200x = 1250[/tex]

                         [tex]10x^{2} -200x - 1250 = 0[/tex]

                           [tex]10(x^{2} -20x - 125)\\[/tex] = 0

                          10(x + 5)(x - 25) =0

                                 x = -5      x = 25

- 5 must be discarded since a length cannot be negative.  

Therefore x = 25 in = width of piece of cardboard

            x + 20 = 25 + 20 = 45 in = length of piece of cardboard