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In triangle $XYZ$, $\angle X = 60^\circ$ and $\angle Y = 45^\circ$. Point $D$ lies on $\overline{YZ}$ such that $\overline{DX}$ bisects $\angle ZXY.$ If $XD = 24,$ then find the area of triangle $XYZ$.

Mar 14, 2020

#1
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The "successful" region has half the size of the whole triangle, so by similar triangles, the probability that the area of triangle XYD is at most 12 is 1/4.

Mar 14, 2020
#2
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Can you please explain this? I'm not sure I understand.

Guest Mar 14, 2020