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:
48 meters
Step-by-step explanation:
The first thing is to calculate the scale, since we know both widths it is possible:
we pass the 9 meters to centimeters = 900 cm
900/6 = 150
So the scale would be 1: 150
Which means that the length is 150 times bigger.
10 * 150 = 1500cm or what equals 15m
the perimeter is the sum of all the sides, therefore:
P = 15 + 15 + 9 + 9
P = 48
Which means that the perimeter of the room is 48 meters
Answer:
x = 110°
Step-by-step explanation:
The sum of the interior angles in a quadrilateral is 360°. This means:
x + x + x - 30 + 1/2x + 5 = 360° - we can simplify this
3 1/2x - 25 = 360° - now add 25 to both sides
3 1/2x = 385 - finally divide both sides by 3 1/2
x = 385 ÷ 3.5 = 110
x = 110°
Hope this helps!
Answer:
You said what now?
Step-by-step explanation:
