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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 = 36, QR = 16, and MY = 50, then find the area of triangle PQR

 Jul 14, 2023
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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 = 36, QR = 16, and MY = 50, then find the area of triangle PQR    

 

Those are the lengths of the sides of the triangle, which is all you need to find the area using Heron's Formula.   

 

if a, b, and c are the lengths of the sides: Area = square root of s(s - a)(s - b)(s - c) where s is half the perimeter.   

 

         36 + 36 + 16            88     

s  =  ———————  =  ———  =  44     

                 2                       2            

 

A  =  square root of (44)(44 – 36)(44 – 36)(44 – 16)    

 

A  =  square root of (44)(8)(8)(28)    

 

A  =  square root of 78,848     

 

A  =  280.8 square units    

.

 Jul 16, 2023

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