Question 934712


find the values of {{{x}}} and {{{y}}} in the parallelogram PQRS:

in the parallelogram opposite sides are equal in length
 
if {{{PT=y}}} and {{{TR=5x+1}}} equal, we have

{{{y=5x+1}}}.............eq.1

if {{{QT=2y}}} and {{{TS=6x+10}}}equal, we have

{{{2y=6x+10}}}.............eq.2

solve the system:

{{{y=5x+1}}}.............eq.1
{{{2y=6x+10}}}.............eq.2....both sides divide by {{{2}}}
___________________________________

{{{y=5x+1}}}.............eq.1
{{{y=3x+5}}}.............eq.2
_______________________________subtract 2 from 1

{{{y-y=5x+1-3x-5}}}

{{{0=2x-4}}}

{{{4=2x}}}

{{{4/2=x}}}

{{{highlight(x=2)}}}

find {{{y}}}

{{{y=5*2+1}}}.............eq.1

{{{highlight(y=11)}}}

sides length will be:

{{{PT=11}}} and 
{{{TR=11}}}

{{{QT=22}}} and 
{{{TS=22}}}