Question

A shipping company is creating their own shipping boxes. They have created a box with a volume of 800in^3, a helght of 8 inches and a base perimeter of 40 inches.

The machine malfunctioned, and in order to be fixed the correct dimensions of the box needed to be input. What length and width would a worker need to input in
order to fix the machine?

Length:?
inches width:?​

Answer 1

Length=10 Inches

Width=10 Inches

Explanation:

Volume of the box
`=800in^3`

Height=8 Inches

Base Perimeter =40 Inches

Volume of a box=lbh

SInce h=8 in, V=800.

Then:

8bl=800

bl=100

`l=(100)/(b)`

Base Perimeter=40 Inches

Perimeter of the Base= 2(l+b)

Therefore: 2(l+b)=40

Substituting
`l=(100)/(b)`

`2((100)/(b)+b)=40\\(100+b^2)/(b)=20\\$Cross Multiply\\100+b^2=20b\\b^2-20b+100=0\\$Solving the quadratic equation \\b^2-10b-10b+100=0\\b(b-10)-10(b-10)=0\\(b-10)(b-10)=0\\b-10=0 (Twice)\\b=10 \:Inch`

Recall:

`l=(100)/(b)=(100)/(10)\\l=10 Inch`

Therefore:

Length=10 Inches

Width=10 Inches