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The total surface area of a box is 100. The length of the box is twice its width, as well as 3 less than its height. How many units are in the height of the box?

 Feb 13, 2020
 #1
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Set up variables

 

Length = 6x

Width = 3x

Height = 6x - 3

 

Commence calculations

 

For surface areas:

L * W surfaces = \(36x^2\)

L * H surfaces = \(72x^2-36x\)

W * H surfaces = \(36x^2-18x\)

 

Set up equation

\(144x^2-54x = 100\)

 

\(144x^2-54x - 100 = 0\) divide by 2

 

\(72x^2-27x-50=0\)

 

72x^2-27x-50=0 = {x=(25/24), x=-((2/3))}

 

So \(x=25/24\)

 

now solve for height

 Feb 13, 2020
edited by CalculatorUser  Feb 13, 2020
edited by CalculatorUser  Feb 13, 2020

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