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

Guest Jul 14, 2023

#1**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 *

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**

_{.}

Bosco Jul 16, 2023