Answer:
Length=10 Inches
Width=10 Inches
Step-by-step explanation:
Volume of the box [tex]=800in^3[/tex]
Height=8 Inches
Base Perimeter =40 Inches
Volume of a box=lbh
SInce h=8 in, V=800.
Then:
8bl=800
bl=100
[tex]l=\frac{100}{b}[/tex]
Base Perimeter=40 Inches
Perimeter of the Base= 2(l+b)
Therefore: 2(l+b)=40
Substituting [tex]l=\frac{100}{b}[/tex]
[tex]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[/tex]
Recall:
[tex]l=\frac{100}{b}=\frac{100}{10}\\l=10 Inch[/tex]
Therefore:
Length=10 Inches
Width=10 Inches
