Answer:
[tex]L=2.3\ ft\\W=1.9\ ft\\H=1.7\ ft[/tex]
Step-by-step explanation:
we know that
The volume of a portable kennel (rectangular prism) is equal to
[tex]V=LWH[/tex]
where
[tex]L=(x+0.4)\ ft\\W=x\ ft\\H=(x-0.2)\ ft[/tex]
[tex]V=7.4\ ft^3[/tex]
substitute the given values in the formula of volume
[tex]7.4=(x+0.4)(x)(x-0.2)[/tex]
Apply distributive property right side
[tex]7.4=x(x^2-0.2x+0.4x-0.08)[/tex]
[tex]7.4=x(x^2+0.2x-0.08)[/tex]
[tex]7.4=x^3+0.2x^2-0.08x[/tex]
[tex]x^3+0.2x^2-0.08x-7.4=0[/tex]
Solve the cubic equation by graphing
using a graphing tool
The solution is x=1.9
see the attached figure
Find the dimensions
substitute the value of x
[tex]L=(1.9+0.4)=2.3\ ft\\W=1.9\ ft\\H=(1.9-0.2)=1.7\ ft[/tex]
