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?

Guest Feb 13, 2020

#1**+3 **

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

CalculatorUser Feb 13, 2020