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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.

 Nov 29, 2022
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You can find the area of the triangle by using Hero's formula:  Area  =  sqrt( s · (s - a) · (s - b) · (s - c) )  where  s  =  (a + b + c) / 2.

 

For this triangle:  a = 36     b = 22     c = 26     --->     s  =  (36 + 22 + 26) / 2  =  42

 

Area  =  sqrt( 42 · (42 - 36) · (42 - 22) · (42 - 26 )  =  sqrt( 42 · 6 · 20 · 16 )  =   .....                   

 

All the other information can be ignored ... anyway, where is point A?

 Nov 29, 2022

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