1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Alja [10]
2 years ago
6

Two altitudes of a triangle have lengths $12$ and $14$. What is the longest possible integer length of the third altitude

Mathematics
1 answer:
nataly862011 [7]2 years ago
8 0

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:

  • a < b+c

2A/12 < 2A/14 + 2A/h

Solve it and get

h<84

  • b < a+c

2A/14 < 2A/12 + 2A/h

Solve it and get

h > -84

  • c < a+b

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.

Learn more about TRIANGLE here brainly.com/question/2217700

#SPJ4

You might be interested in
The following table shows the first segment of a five-year amortization schedule.
ELEN [110]

After one year of payments, the amount need to be paid to interest is $1100.42 if the first segment of a five-year amortization schedule is a 5-year amortization schedule option (a) is correct.

<h3>What is a loan amortization schedule?</h3>

It is defined as the systematic way of representation of loan payments according to the time in which the principal amount and interest mentioned in a list manner.

We have a table given that showing a first segment of a five-year amortization schedule that has a 5-year amortization schedule and the amount of interest paid for months 1 through 12.

As the loan amount is not mentioned in the question, we are assuming the loan amount is $1184.6

Therefore, loan amount = $1184.6

The outstanding amount at the end of one year, which is 12 months, is shown in the table as $84.18

After one year of payments, the amount need to be paid to interest:

= Loan amount - Outstanding amount after 12 months

= 1184.6 - 84.18

= $1100.425

Thus, after one year of payments, the amount need to be paid to interest is $1100.42 if the first segment of a five-year amortization schedule is a 5-year amortization schedule option (a) is correct.

Learn more about the amortization schedule here:

brainly.com/question/15357884

4 0
2 years ago
paulette has arrived at cape horn. there are five penguins waiting to cross over to antarctica. jim goes before john but after j
Nikolay [14]

Well, this is a guess. Jim goes before john, but after joe. So Jim is second. John is third, so that leaved Joe.

Joe, Jim, John. But I don't know about the other 2.

---

sorry if this doesn't help

6 0
2 years ago
Two planes left an airport at noon. One flew east at a certain speed and the other flew west at twice the speed. The planes were
12345 [234]
The plane flying west was flying at 600 miles per hour and the plane flying east was flying 300 miles per hour
7 0
3 years ago
15 points. Please help meeee
yaroslaw [1]

Answer:

B.

Step-by-step explanation:

5 0
3 years ago
Read 2 more answers
Question 35 of 40
andreyandreev [35.5K]

Answer:

120(0.96)^n

Step-by-step explanation:

6% = 0.06

1 - 0.06 = 0.94

p = 120(0.96)^n

7 0
3 years ago
Other questions:
  • How do you simplify the expression (y-15)5
    11·1 answer
  • Roger has 47 cars. Can he group the cars in more than 2 ways?
    12·1 answer
  • Jake volunteers to help out his younger brother's basketball team in his free time. One of his tasks is to ensure that all the b
    12·1 answer
  • Jen goes to a carnival with $25.00 to spend.
    13·1 answer
  • The cost of three tickets to a movie is at least $20. Select an inequality that represents the cost x (in dollars) of each ticke
    11·1 answer
  • I will mark brainliest to whoever answers most accurately)
    13·2 answers
  • How many edges are there?
    7·1 answer
  • Sheleah and her family are planning a trip from Los Angeles, California to Melbourne, Australia. While booking her family's plan
    13·2 answers
  • Please help I’ll give 40 extra points!!!
    14·2 answers
  • Mrs. Buchanan is planning marching routines for the school band. The band has 36 members. Band
    9·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!