please help 10 pointsThe height and width of a rectangular prism are each 2 inches shorter than the length of the prism. The volume of the prism is 40 cubic inches. Approximate the dimensions of the prism to the nearest hundredth. Show work.

Answer:The length of the prism is 4.87 inchesThe width of the prism is 2.87 inchesThe height of the prism is 2.87 inchesStep-by-step explanation:Letl -----> the length of the prism in inchesw ----> the width of the prism in inchesh---> the height of the prism in incheswe know thatThe 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 Csubstitute 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 graphingusing a graphing toolThe solution is l=4.87 insee the attached figureFind 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 areThe length of the prism is 4.87 inchesThe width of the prism is 2.87 inchesThe height of the prism is 2.87 inches