+1415 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
+137 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
