Answer:
The length of the prism is 4.87 inches
The width of the prism is 2.87 inches
The height of the prism is 2.87 inches
Step-by-step explanation:
Let
l -----> the length of the prism in inches
w ----> the width of the prism in inches
h---> the height of the prism in inches
we know that
The volume of the prism is
[tex]V=lwh[/tex]
we have
[tex]V=40\ in^3[/tex]
so
[tex]40=lwh[/tex] -----> equation A
[tex]w=l-2[/tex] ----> equation B
[tex]h=l-2[/tex] -----> equation C
substitute equation B and equation C in equation A and solve for l
[tex]40=l(l-2)(l-2)\\\\40=l(l^{2}-4l+4)\\\\40=l^{3}-4l^{2}+4l\\\\l^{3}-4l^{2}+4l-40=0[/tex]
Solve the cubic equation by graphing
using a graphing tool
The solution is l=4.87 in
see the attached figure
Find the value of w
[tex]w=4.87-2=2.87\ in[/tex]
[tex]h=4.87-2=2.87\ in[/tex]
The approximate dimensions of the prism are
The length of the prism is 4.87 inches
The width of the prism is 2.87 inches
The height of the prism is 2.87 inches
