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Scilla [17]
3 years ago
5

A cookie company packages its cookies in rectangular prism boxes designed with square bases that have both a length and width of

4 inches less than the height of the box. Find the dimensions of the box if its volume is 128 cubic inches.
Mathematics
1 answer:
Verdich [7]3 years ago
7 0

Answer:

length and width=4

height=8

Step-by-step explanation:

Hello to solve this problem we must propose a system of equations of 3x3, that is to say 3 variables and 3 equations.

Ecuation 1

Leght=Width

.L=W

Ecuation 2

To raise the second equation we consider that the length and width of 4 inches less than the height of the box

H-4=W

Ecuation 3

To establish equation number 3, we find the volume of a prism that is the result of multiplying length, width, and height

LxWxH=128

From ecuation 1(w=h)

HW^2=128

solving for  H

H=\frac{128}{W^2}

<em />

<em>Using ecuation 2</em>

H-4=W

\frac{128}{W^2}-4=W\\W^3+4W^2-128=0

Now we find the roots of the equation, 2 of them are imaginary, and only one results in 4

W=4in

L=4in

to find  the height we use the ecuation 2

H-4=W

H=4+W

H=4+4=8

H=8IN

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