Question 1157189


 If {{{EFGH}}} is an isosceles trapezoid,

if

{{{EH=4x-27 }}}
{{{FG=x+9 }}}
{{{EG=3y+19}}}
{{{FH=11y-21}}}

then  {{{EH=FG}}} and {{{EG=FH}}}

set up equations:

{{{4x-27=x+9}}} .......solve for {{{x}}}
{{{4x-x=27+9}}}
{{{3x=36}}}
{{{x=36/3}}}
{{{x=12}}}


{{{3y+19=11y-21}}}.......solve for {{{y}}}
{{{11+19=11y-3y}}}
{{{30=8y}}}
{{{y=30/8}}}
{{{y=15/4}}}
{{{y=3.75}}}


 so,{{{x=12}}} and {{{y=3.75}}}

you can also check the length of equal sides and equal diagonals:

{{{EH=4*12-27 =21}}}
{{{FG=12+9 =21}}}
{{{EG=3(3.75)+19=30.25}}}
{{{FH=11(3.75)-21=30.25}}}