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spayn [35]
3 years ago
15

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:?​
Mathematics
1 answer:
Kazeer [188]3 years ago
8 0

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

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