Answer:
AH = 1 or 4
CH = 4 or 1
Step-by-step explanation:
An altitude divides a right triangle into similar triangles. That means the sides are in proportion, so ...
AH/BH = BH/CH
AH·CH = BH²
The problem statement tells us AH + CH = AC = 5, so we can write
AH·(5 -AH) = BH²
AH·(5 -AH) = 2² = 4
This gives us the quadratic ...
AH² -5AH +4 = 0 . . . . in standard form
(AH -4)(AH -1) = 0 . . . . factored
This equation has solutions AH = 1 or 4, the values of AH that make the factors be zero. Then CH = 5-AH = 4 or 1.
It's approximately 0.0032
For calculating the mean, you want to add up all of the numbers then divide by how many numbers there are. So you'd do:
5+10+12+4+6+11+13+5 then divide that by 8
The answer to your question is: 8.25