Question

Given that PS is the perpendicular bisector of QR, PQ=3.5m+18, and PR=6m+3, identify PQ.

Answer 1

Answer:

$PQ=39\ units$

Step-by-step explanation:

we know that

$QS=RS$ ----> equation A

Applying Pythagoras Theorem

$PQ^2=SP^2+QS^2$ -----> equation B

$PR^2=SP^2+RS^2$-----> equation C

substitute equation A in equation C

$PR^2=SP^2+QS^2$

we have that

$PR^2=PQ^2$

so

$PR=PQ$

substitute the given values

$6m+3=3.5m+18$

Solve for m

$6m-3.5m=18-3$

$2.5m=15$

$m=6$

Find the value of PQ

$PQ=3.5m+18$

substitute the value of m

$PQ=3.5(6)+18$

$PQ=39\ units$

Answer 2

Answer:

39

Step-by-step explanation:

Triangles PQS and PRS are congruent

PQ = PR

3.5m + 18 = 6m + 3

2.5m = 15

m = 6

PQ = 3.5(6) + 18

PQ = 39