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In triangle PQR, M is the midpoint of PQ. Let X be the point on QR such that PX bisects angle QPR, and let the perpendicular bisector of PQ intersect AX at Y. If PQ = 36, PR = 22, QR = 26, and MY = 8, then find the area of triangle PQR

 Oct 23, 2024
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our given data that was provided:

 

data:

pq = 36

pr = 22

qr = 26

M is the mid point, pm = mq = 18

my = 8

 

we can use a formula known as the heron formula to find the area for triangle pqr:

 

find the semi perimeter of our triangle:

s =   [ pq + pr + qr 2 / { 36 + 22 + 26 {2} = 42

 

which will equal:

sqrt s/s - pq ( s - pr )( s - pr )( s -qr )  = sqrt 42( 42-36 ) ( 42 - 22 ) ( 42 - 26 ) = sqrt 42 x 6 x 20 x 16 = sqrt ( 80640 = 40 sqrt 14 ) 

 

front the info we get:

 

pqr is 40 sqrt 14

 Oct 23, 2024

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