Answer:
The dimensions of the box are
\(2,6,7\)
Step-by-step explanation:
we know that
The volume of a box in the shape of a cube is equal to
\(V=W*L*H\)
where
W is the width of the box
L is the length of the box
H is the height of the box
In this problem we have
\(V=84\ ft^{3}\)
\(W=x\ ft\)
\(L=x+1\ ft\)
\(H=x-4\ ft\)
Substitute the values in the formula of volume
\(84=x*(x+1)*(x-4)\)
\(84=(x^{2}+x)*(x-4)\\84=x^{3} -4x^{2}+x^{2}-4x\\84=x^{3}-3x^{2}-4x\\x^{3}-3x^{2}-4x-84=0\)
Using a graphing tool
Solve the cubic function
see the attached figure
The value of x is equal to
\(x=6\ ft\)
the dimensions of the box are
\(W=x\ ft=6\ ft\)
\(L=x+1\ ft=6+1=7\ ft\)
\(H=x-4\ ft=6-4=2\ ft\)
