Question 1154093

The perimeter of parallelogram {{{ABCD }}}is {{{96cm}}}. 

{{{AD}}} is {{{6cm}}} more than {{{twice}}} {{{AB}}}. 

so, {{{AD=2AB+6}}}.....eq.1

in parallelogram opposite sides are equal in length:

{{{AB=CD}}}
{{{AD=BC}}}=>{{{BC=2AB+6}}}

{{{P=96cm}}}

{{{AB+CD+AD+BC=96}}}.....substitute {{{AB=CD}}},{{{AD}}} and {{{BC}}} from eq.1

{{{AB+AB+2AB+6+2AB+6=96}}}

{{{6AB+12=96}}}

{{{6AB=96-12}}}

{{{6AB=84}}}

{{{AB=84/6}}}

{{{highlight(AB=14)}}} => also {{{highlight(CD=14)}}}


go to eq.1

{{{AD=2AB+6}}}.....eq.1, substitute {{{AB}}}

{{{AD=2*14+6}}}

{{{highlight(AD=34)}}}=> also {{{highlight(BC=34)}}}


check the perimeter:

{{{AB+CD+AD+BC=96}}}
{{{14+14+34+34=96}}}
{{{96=96}}}