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
MrMuchimi
2 years ago
5

Charla has six segments with which to make two triangles. The segments lengths are 2 in., 3 in., 4 in., 5 in., 6 in., and 7 in.

Which are possible side lengths of her two triangles?
Mathematics
2 answers:
iVinArrow [24]2 years ago
6 0

Answer:

The possible lengths are:

2,3,4 and 5, 6, 7;

2,4, 5 and 3, 6, 7

2,6,7 and 3,4,5

Step-by-step explanation:

Because of the triangle inequality, we know that for any given triangle, the sum of two of its sides is always greater than the other side. And this is true for any two sides we pick.

Now we have segments of 2,3,4, 5, 6 and 7 inches long. So now we have to pair this segments into two groups of three in which the sum of two elements of each group is greater than the third element of said group.

There are 20 ways of choosing 3 elements out of a group of 6 elements, however, you should notice that the choosing of 2,3,4 is the same as the choosing of 5,6,7 (since by choosing any three elements for our first triangle the elements for our second one are determined and vice versa) Thus, we only have 10 different options to choose.

Option 1: 2, 3, 4 and 5, 6, 7

2 + 3 > 4

2 + 4 > 6

3 + 4 > 2

and

5 + 6 > 7

5 + 7 > 6

6 + 7 > 5

Thus, this is a possible side length of her two triangles

Option 2: 2,3,5 and 4, 6, 7

2 + 3 = 5

Thus, this is not a possible side length because it doesn't fit the inequality.

Option 3: 2,3, 6 and 4,5,7

2 + 3 < 6

Thus this is not an option.

Option 4: 2,3, 7 and 4,5 6

2 + 3 < 7

Thus, this is not an option either

Option 5: 2,4, 5 and 3, 6, 7

2 + 4 > 5

2 + 5 > 4

4 + 5 > 2

and

3 + 6 > 7

3 + 7 > 10

6 + 7 > 3

Thus, this is an option.

Option 6: 2,4, 6 and 3, 5, 7

2 + 4 = 6 therefore this is not an option.

Option 7: 2, 4, 7 and 3, 5, 6

2 + 4 < 7 thus this is not an option.

Option 8: 2, 5, 6 and 3, 4, 7

3 + 4 = 7, thus this is not an option

Option 9: 2, 5, 7 and 3, 4, 6

2 + 5 = 7, thus this is not an option.

Option 10: 2, 6, 7 and 3, 4, 5

2 + 6 > 7

2 + 7 > 6

7 + 6 > 2

and

3 + 4 > 5

3 + 5 > 4

4 + 5 > 3

Thus this is an option.

Therefore, our possible lengths are: 2,3,4 and 5, 6, 7; 2,4, 5 and 3,6,7; 2,6,7 and 3,4,5

Leni [432]2 years ago
3 0

Answer:

2 in., 3 in., 4 in. and 5 in., 6 in., 7 in.

Step-by-step explanation:


You might be interested in
Given the data 14,26,23,19,24,46,15,21: a.what is the outlier in the data? b. What is the mean with the outlier? c. What is the
Olegator [25]
The outlier is the piece of data that does not fit the general data set. In this case, 46 is much higher than all of the other numbers. This is the outlier.
3 0
3 years ago
Which would be the correct answer!
Blizzard [7]

Answer:

I think also option c ok

8 0
3 years ago
Help please!(picture)
UkoKoshka [18]

Answer:

7a - 2

Step-by-step explanation:

A perimeter is just the sum of all sides added together, so just put all the expressions together into a big equation.

2a - 3 + 2a + 3a + 1

Combine like terms

7a - 2

5 0
3 years ago
What is the difference of the polynomials?
Olenka [21]
(5x³ + 4x²) - (6x² - 2x - 9)

-1(6x²) -1(-2x) -1(-9) = -6x² + 2x + 9

5x³ + 4x² - 6x² + 2x + 9

5x³ - 2x² + 2x + 9  Choice D.


8 0
2 years ago
Read 2 more answers
The sum of two numbers is 67. if one of the numbers is p, express the other number in terms of p
Ierofanga [76]
Since the sum of two numbers is 67
and one number is p
so the other number is (67-p)
3 0
2 years ago
Other questions:
  • In circle O, what is the measure of angle MAJ
    7·2 answers
  • Another one, I’ve been stuck for 2 weeks now
    10·1 answer
  • Daniel has $600 in a checking account, has $12,000 in a savings account,
    13·2 answers
  • A right rectangular prism has a length of 6 cm, a width of 2 cm, and a height of 5 cm. What is the surface area of the prism?
    5·1 answer
  • Barry is thinking of a number that is greater than -7 and less than -6 3/4. which numbers could be Barry's number? Select all th
    12·1 answer
  • PEOPLE WHO WORKS IN BRAINLY PLS PLS PLS DELETE impoopsock ACCOUNT HE IS POSTING NASTY INNOPORIATE STUFF I JUST SEEN ONE A MIN AG
    7·1 answer
  • 100 points!!What is the equation of the line with points represented in the table? What can yoy conclude about the line represen
    9·1 answer
  • PLEASE HELP ASAP- What is the value of AB?
    11·1 answer
  • The perimeter of a rectangle is 84 cm. If the length is 17 cm, how wide is the rectangle?
    6·1 answer
  • If 15% of 200 apples are bad, how many apples are bad?
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!