Answer:
Length is 20 in
Height is 4 in
Step-by-step explanation:
we are given
The width of a rectangular box is 8in
so, [tex]W=8[/tex]
The height is one fifth the length
Let's assume length =x
L=x
[tex]H=\frac{1}{5}x[/tex]
now, we can find volume
[tex]V=L\times W\times H[/tex]
we can plug
[tex]640=x\times 8\times \frac{1}{5}x[/tex]
now, we can solve for x
[tex]\frac{8}{5}x^2=640[/tex]
[tex]x^2=400[/tex]
[tex]x=20[/tex]
so, L=20 in
[tex]H=\frac{1}{5}\times 20[/tex]
[tex]H=4[/tex]
So,
Length is 20 in
Height is 4 in
