Question 935001
{{{PS}}} is the perpendicular bisector of {{{QR}}},

{{{PQ=4x+19}}}

{{{PR=2x+32}}}

find: {{{PQ}}}

since triangle {{{PQR}}} is an isosceles triangle, {{{PQ=PR}}}

then  we have {{{4x+19=2x+32}}} ...solve for {{{x}}}


{{{4x-2x=32-19}}}

{{{2x=13}}}

{{{x=13/2}}}

{{{x=6.5}}}

so, since {{{PQ=4x+19}}}, plug in {{{x=6.5}}}

{{{PQ=4*6.5+19}}}

{{{PQ=26+19}}}

{{{highlight(PQ=45)}}}