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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 -12 inch squares from each corner. The length of the original piece of cardboard is 24 inch more than the width. If the volume of the box is 1740 inch , determine the dimensions of the original piece of cardboard.

Respuesta :

jmonterrozar

Answer:

29 feet in length, 5 feet in width and 12 feet in height

Step-by-step explanation:

We have that for the volume of a quadrangular prism is:

V = l * w * h

Ie length times width times height

In this case, the height is determined by the squares that you put in each corner, taking into account that a square has all the same sides, the height is 12 inches. h = 12

they tell us that the length is 24 inches more than the width, that is, l = 24 + w

replacing we have:

1740 = (24 + w) * w * 12

1740 = 12 * w ^ 2 + 288 * w

12 * w ^ 2 + 288 * w - 1740 = 0

if we calculate the root, we have w = 5 or w = -29

only works when w = 5

Thus:

l = 24 + 5

l = 29

which means that the dimensions are:

29 feet in length, 5 feet in width and 12 feet in height

29 feet in length, 5 feet in width and 12 feet in height

  • The calculation is as follows;

The volume of a quadrangular prism is:

[tex]V = l \times w \times h[/tex]

The length is 24 inches more than the width,

So l = 24 + w

Now

[tex]1740 = (24 + w) \times w \times 12\\\\1740 = 12 \times w ^ 2 + 288 \times w\\\\12 \times w ^ 2 + 288 \times w - 1740 = 0[/tex]

if we calculate the root, we have w = 5 or w = -29

only works when w = 5

So,

l = 24 + 5

l = 29

Learn more: https://brainly.com/question/13981855?referrer=searchResults

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