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I woule like a proper explaination please! Not just the answer!



In triangle \(PQR, M\) is the midpoint of \( \overline{PQ}\) Let \(X\) be the point on \(\overline{QR}\) such that \(\overline{PX}\) bisects \(\angle{QPR}\) and let the perpendicular bisector of \(\overline{PQ}\) intersect \(\overline{PX}\) at \(Y\) If  \(PQ = 36\) and \(MY = 8\) then find the area of triangle \(PYR.\)

 Jul 5, 2023
 #1
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-1

Here are the steps to solve the problem:

Since M is the midpoint of PQ, then QM = 18.

Since PX bisects angle QPR, then PX = QR/2 = 19.

Since Y is on the perpendicular bisector of PQ, then PY = QY = 18.

Since MY = 8, then PY = 18 - 8 = 10.

Since PX = 19 and PY = 10, then triangle PXY is a 9-10-11 right triangle.

Since the perpendicular bisector of PQ intersects PX at Y, then PY is an altitude of triangle PQR.

Therefore, the area of triangle PYR is (1/2)(PQ)(PY) = (1/2)(36)(10) = 180.

Therefore, the area of triangle PYR is 180.

 Jul 5, 2023
 #4
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0

 

 

>>>>> is a 9-10-11 right triangle <<<<<  

 

I don't know about the rest of the answer, but 9-10-11 is not a right triangle.  

Guest Jul 5, 2023
 #2
avatar+197 
0

that wasn't correct...

 Jul 5, 2023
 #3
avatar+197 
+2

nvm...i found the answer...it's 88

 Jul 5, 2023

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