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

Answer:

Length=10 Inches

Width=10 Inches

Step-by-step 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

$l=\frac{100}{b}$

Base Perimeter=40 Inches

Perimeter of the Base= 2(l+b)

Therefore: 2(l+b)=40

Substituting $l=\frac{100}{b}$

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

Recall:

$l=\frac{100}{b}=\frac{100}{10}\\l=10 Inch$

Therefore:

Length=10 Inches

Width=10 Inches