Question 747317

rectangle with perimeter {{{2x+2*W=20cm}}} where {{{W}}} is the width and
{{{x}}} is the length

if diagonal {{{d=8cm}}} then {{{d^2=W^2+x^2}}} => {{{64cm^2=W^2+x^2}}}

{{{2x+2*W=20cm}}}..eq.1...solve for {{{x}}}..divide all terms by {{{2}}}


{{{x+W=10cm}}}

{{{x=10cm-W}}}.....plug in {{{64cm^2=W^2+x^2}}}

{{{64cm^2=W^2+(10cm-W)^2}}}......solve for {{{W}}}

{{{64cm^2=W^2+100cm^2-20W+W^2}}}

{{{2W^2-20W+100cm^2-64cm^2=0}}}

{{{2W^2-20W+36cm^2=0}}}.....divide all terms by {{{2}}}

{{{W^2-10W+18cm^2=0}}}

{{{W = (-(-10) +- sqrt( (-10)^2-4*1*18 ))/(2*1) }}}

{{{W = (10 +- sqrt(100-72 ))/2 }}}

{{{W = (10 +- sqrt(28))/2 }}}

{{{W = (10 +- sqrt(4*7))/2 }}}

{{{W = (10 +- 2sqrt(7))/2 }}}

{{{W =5 +- sqrt(7) }}}

so, {{{W =5 + sqrt(7)=7.65cm }}} or {{{W =5 + sqrt(7)=2.35cm }}}

now find {{{x}}}

{{{x=10cm-W}}}

{{{x=10cm-7.65cm=2.35cm}}} or {{{x=10cm-2.35cm=7.65cm}}}


so, we will take the length {{{highlight(x=7.65cm)}}} and the width {{{highlight(W =2.35cm) }}}


now show {{{x^2 - 10x +18 = 0}}}

{{{(7.65)^2 - 10*7.65 +18 = 0}}}

{{{58.5225 - 76.5 +18 = 0}}}

{{{58.5+18 - 76.5 = 0}}}

{{{76.5 - 76.5 = 0}}}

{{{0= 0}}}