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A rectangular piece of metal is 10 in longer than it is wide. Squares will side 2 in long are cut from the four corners and the flaps are fielded upward to form an open box. If the volume of the box is 1008 in^3, what were the original dimensions of the piece of mental

Respuesta :

The original dimensions of the piece of metal are; 22 inches is the width of the rectangular metal and 32 inches is the length.

How to Maximize Volume?

Let x = the width of the rectangular piece of metal

then

(x + 10) = the length

Removing the 2 inches squares would make the dimensions of the box:

(x - 4) by (x + 10-4) or (x - 4) by (x + 6)

The height of the box = 2 inches

The volume equation is; V = L * W * h

Thus;

(x + 6) * (x - 4) * 2 = 1008

divide both sides by 2

(x + 6)(x - 4) = 504

FOIL

x² - 4x + 6x - 24 = 504

x² + 2x - 24 - 504 = 0

x² + 2x - 528 = 0

Using quadratic equation calculator, this will factor to

(x + 24)(x - 22) = 0

We will pick the positive solution;

x = 22 inches is the width of the rectangular metal

then

32 inches = the length

Read more about Maximizing Volume at; https://brainly.com/question/26306190

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