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 = 22, QR = 26, and MY = 8, then find the area of triangle PQR.

Guest Feb 18, 2023

#1**0 **

You can just use the herons formula: \(\frac{\sqrt{s(s-a)(s-b)(s-c)}}{2}\)

s = semi perimeter

a = side 1

b = side 2

e = side 3

if you plug in the values from the problem you get, \(\frac{\sqrt{84(48)(62)(58)}}{2}\)

or \(\frac{\sqrt{14499072}}{2}\)

but we can simplify that further, because 14499072 is in a sqrt, dividing by two is just dividing by 4 inside of the sqrt so \(\sqrt{3624768}\)

and that is our answer!

Guest Feb 18, 2023