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# I NEED HELP ASAP!!!!!

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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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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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>>>>> 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
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that wasn't correct...

Jul 5, 2023
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