+0  
 
0
16
5
avatar

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 19, 2023
 #1
avatar
0

Upload the picture of your triangle. If they don't have one, then learn to draw one and uploaded.

 Jul 19, 2023
 #2
avatar
+1

You're expecting too much of these homework cheaters.

Guest Jul 19, 2023
 #3
avatar+570 
0

 

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   

 

We don't need all those midpoints and angle bisectors and whatever MY is.   

We have the three sides of a triangle, and that's all we need to find its area.  

We could still get the area, but it's an isoceles triangle, and that makes it easier.  

 

The sides:     PQ = 36, PR = 36, QR = 16     

This tells us that triangle PQR is an isoceles triangle, with angle P at the apex.  

 

So drop a perpendicular line from P down to base QR, intersect at point J.   

This does two things.  It bisects QR and it creates two right triangles.    

 

So use Pythagoras' formula to determine the length of this perpendicular,  

which, conveniently for us, is also the height of PQR.  

 

PJ2 = 362 – 82    ----->   PJ2 = 1296 – 64   ----->    PJ = 35.1   

 

Area of PQR  =  (1 / 2) • base • height  =  (1 / 2) • 16 • 35.1  =  280.8    

 

check answer    

 

per Heron's Formula, Area  =  sqrt of (44)(8)(8)(28)  = sqrt(78,848)  =  280.8   

 

Confirmed.  I love it when a plan comes together.    

.

 Jul 20, 2023
 #4
avatar
+1

Ron, this is an excellent presentation!

 

 GA

--. .- 

Guest Jul 20, 2023
 #5
avatar+570 
0

 

Praise from Caesar.  Thank you.  Say goodnight, Ginger.  :-)   hehe a little joke 

.

Bosco  Jul 20, 2023

3 Online Users

avatar
avatar