Since PS is the perpendicular bisector of QR, it divides QR into two equal parts, and it is also perpendicular to QR.
Given:
PQ=4x+19
PR=2x+32
Since PS is the perpendicular bisector of QR, we have:
PQ=QR=PR
Therefore, we can set up an equation using the given lengths of PQ and PR:
4x+19=2x+32
solve for x:
2x=13
x=13/2
Now that we have the value of x, we can find PQ using the given expression PQ=4x+19:
PQ=4
. 13/2+19=26+19=45
so, the length of PQ is 45.