The longest possible altitude of the third altitude (if it is a positive integer) is 83.
According to statement
Let h is the length of third altitude
Let a, b, and c be the sides corresponding to the altitudes of length 12, 14, and h.
From Area of triangle
A = 1/2*B*H
Substitute the values in it
A = 1/2*a*12
a = 2A / 12 -(1)
Then
A = 1/2*b*14
b = 2A / 14 -(2)
Then
A = 1/2*c*h
c = 2A / h -(3)
Now, we will use the triangle inequalities:
2A/12 < 2A/14 + 2A/h
Solve it and get
h<84
2A/14 < 2A/12 + 2A/h
Solve it and get
h > -84
2A/h < 2A/12 + 2A/14
Solve it and get
h > 6.46
From all the three inequalities we get:
6.46<h<84
So, the longest possible altitude of the third altitude (if it is a positive integer) is 83.
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Answer:
- 5/11
Step-by-step explanation:
The answer would be b because you are just multiply
<span>f(x)=3-2x
</span><span>f(8)=3-2(8) = 3 -16 = -13
</span><span>g(x)=1/x+5
</span><span>g(8)=1/8+5 = 1/8 + 40/8 = 41/8
</span><span>[f/g](8) = -13 / (41/8) = -13 * (8/41) = -104/41 = -2 22/41</span>
