A point P is chosen at random within right triangle ABC. Find the probability that the area of triangle PBC is less than half of the area of triangle ABC.

Guest Dec 29, 2021

#1**+1 **

Draw a line through P that is parallel to BC.

If P is "below" that line, the area of triangle(PBC) will be less than one-half the area of triangle(ABC).

The area below that line is three times the area above the line, so the probability that the area of

triangle(PBC) is less than the area of triangle(ACB) is 3/4.

geno3141 Dec 29, 2021