Question 1133295


given:


{{{V=180.4in^3}}} 


The length {{{L=h- 3.2in}}}


 its width is{{{W= 2.3in}}} 


Find the height {{{h}}} and length {{{L }}} of the box to the nearest tenth.


{{{V=L*W*h}}} ...substitute {{{L}}} and {{{W}}}


{{{L*W*h=180.4in^3}}} 


{{{(h- 3.2in)2.3in*h=180.4in^3}}} 


{{{(h- 3.2in)*h=180.4in^3/2.3in}}} 


{{{h^2- 3.2in*h=78.44in^2}}} 


{{{h^2- 10.6in*h+7.4in-78.44in^2=0}}} 


{{{(h^2- 10.6in*h)+(7.4in*h-78.44in^2)=0}}}


{{{h(h- 10.6in)+7.4in(h-10.6in)=0}}}


{{{(h - 10.6in) (h + 7.4in) = 0}}}


solutions:


if {{{(h - 10.6in)  = 0}}} => {{{h=10.6in}}}

if {{{  (h + 7.4in) = 0}}}=> {{{h=-7.4in}}}=> disregard negative solution


so, the height is {{{10.6in}}}

go to

{{{L=h- 3.2in}}} plug in {{{h}}}

{{{L=10.6in- 3.2in}}}

{{{L=7.4in}}}


The length is {{{7.4in}}}