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:
204 ft^2
Step-by-step explanation:
<u>triangle on the left</u>:
A= l x w x 1/2
A = 12 x 5 x 1/2
A = 30 ft^2
<u>triangle on the right</u>:
Same thing
A = 30 ft^2
<u>square in the middle</u>:
A = l x w
A = 12 x 12
A = 144 ft^2
<u>Add them up</u>:
30 + 30 + 144 = 204 ft^2
So the so the product of two consecutive numbers is 4160 or
x(x+1)=4160
distribute
x^2+x=4160
subtract 4160 from both sides
x^2+x-4160=0
find the factor (if you want to know how, just ask in the comments)
(x-64)(x+65)=0
so the answer is x could be 64 or -65
so the number that work are 64,65 and -65,-64
Answer:
sorry i dont know it but can i get brainliest i never got it
Step-by-step explanation:
Answer:
3.
141592653589793238462643383279502884197169399375105
82097494459230781640628620899862803482534211706798
21480865132823066470938446095505822317253594081284
81117450284102701938521105559644622948954930381964
42881097566593344612847564823378678316527120190914
5648566923460348610454326648213393607260249141273
Step-by-step explanation:
:)
