Question

If QT is the perpendicular bisector of PR, find the measure of each.

Answer 1

Answer:

x = 7

y = 12

PQ = QR = 29

Step-by-step explanation:

In ΔPSR , PS = SR (given)

$=> 4x+4=7x-17\\=> 7x-4x=17+4\\=>3x=21\\=>x=\frac{21}{3}=7$

In ΔPQR , QT is perpendicular bisector of PR. So , PT = RT . As ΔPQR has a perpendicular bisector , it is an isosceles triangle.

So,

,$PQ = RQ\\=>5y-31=2y+5\\=>5y-2y=31+5\\=>3y=36\\=>y=\frac{36}{3} =12$