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.

 Dec 30, 2022

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 \(\sqrt{42(42-36)(42-22)(42-26)} = \sqrt{42*8*20*16} = 32\sqrt{105}\)

 Dec 30, 2022

Yeah, I agree with Proyaop, Herons formula is defininently a good way to find triangles!

 Dec 30, 2022

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