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 Dec 30, 2022

#1**+3 **

When looking at the lengths of the sides of the triangle, you realize you can use a certain formula and ignore all the random lines inside the triangle. Heron's formula tells you the area of a triangle given its 3 side lengths.

By heron's formula (which I will not prove and you can look it up on your own), the area of the triangle is \(\sqrt{42(42-36)(42-22)(42-26)} = \sqrt{42*8*20*16} = 32\sqrt{105}\)

proyaop Dec 30, 2022