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
FrozenT [24]
3 years ago
6

Select ALL the sets of three side lengths that will make a triangle.

Mathematics
2 answers:
konstantin123 [22]3 years ago
6 0

Answer:

7 + 6

5 + 11

Step-by-step explanation:

the lengths of the two shorter sides of a triangle must add up to more than the length of the third side.

3 + 4 = 7 ≤ 8    no

7 + 6 = 13 > 12   yes

5 + 11 = 16 > 13  yes

4 + 6 = 10 ≤ 12  no

4 + 6 = 10 ≤ 10  no

Tatiana [17]3 years ago
6 0
<h3>2 Answers:</h3>
  • B) 7, 6, 12
  • C) 5, 11, 13

===================================================

Explanation:

We'll use the triangle inequality theorem. Recall that this theorem says that a triangle is only possible if and only if adding any two sides leads to a sum larger than the third side.

Let's say we had a triangle with sides a,b,c. Such a triangle is only possible if all three conditions hold true

  • a+b > c
  • b+c > a
  • a+c > b

----------------

Let's go through each answer choice to see if those conditions hold up.

  • Choice A. We have a = 3, b = 4, c = 8. Note that a+b = 3+4 = 7 which is <u>not</u> greater than c = 8. Therefore a+b > c is false, and we cannot make a triangle here. We don't need to check the other inequalities. I recommend you trying it out by cutting out slips of paper of these lengths. You'll find a triangle cannot be constructed. We can rule out choice A.
  • Choice B. We have a = 7, b = 6 and c = 12. We can see that a+b = 7+6 = 13 which is larger than c = 12. So far, so good. Then note that b+c = 6+12 = 18 which is larger than a = 7. Finally, a+c = 7+12 = 19 which is larger than b = 6. Picking any two sides, adding them up, leads to a sum larger than the third side. A triangle is possible in this case. Choice B is one of the answers.
  • Choice C. This time a = 5, b = 11, c = 13. You should find that a triangle is possible following the same steps as done in choice B above. Adding any two sides leads to a sum larger than the third side. Choice C is one of the answers.
  • Choice D. Now we have a = 4, b = 6, c = 12. Then note a+b = 4+6 = 10 which is too small compared to c = 12. Meaning a+b > c is false. A triangle isn't possible. Cross choice D off the list.
  • Choice E. In this case, a = 4, b = 6 and c = 10. Adding the first two values gets us a+b = 4+6 = 10 which is <u>not</u> larger than c = 10. If you used slips of paper, you'd find that a straight line is formed rather than a triangle. Cross choice E off the list.

To wrap things up, only choice B and choice C are possible triangles because adding any two sides leads to a sum larger than the third side.

You might be interested in
It costs $5 to become a member of a video game club. After that, video games 10 each with a 7% tax on each game. If you spent $6
Alinara [238K]

Answer:

6 games

Step-by-step explanation:

Each game is 10.70 x 6 = 64.20+5=no change

5 0
3 years ago
Read 2 more answers
Molly had a balance of $72 In her savings account before depositing $25. What is her new balance?
vovangra [49]

Answer:

$97

Step-by-step explanation:

just add 72 and 25 dude

4 0
3 years ago
8p + 2 + 10 + 3p = 67
OLga [1]

Answer:

I'm guessing the answer you are wanting is false

5 0
3 years ago
Find the zero if the function f(x) = 5x-3
Sladkaya [172]
X equal 5/3 set it equal to zero and slove
5 0
3 years ago
Use the graph of the function f to determine the given limit
timofeeve [1]

Answer:

i cant see

Step-by-step explanation:

5 0
3 years ago
Other questions:
  • please help!!! Vance is designing a garden in the shape of an isosceles triangle. The base of the garden is 36 feet long. The fu
    13·1 answer
  • Tom, Aaron, and Harry are camping in their tents. If the distance between Tom and Aaron is 153 feet, the distance between Tom an
    11·1 answer
  • Help.
    11·1 answer
  • A taxi company charges $1.00 for the first mile (or part of a mile) and 20 cents for each succeeding tenth of a mile (or part).
    15·1 answer
  • 8-1- (18 – 2):8<br> help pls
    11·1 answer
  • Translate it and Simplify if needed :Four more than three times a number decreased by six
    10·1 answer
  • Who ever gets this will get a brainlest
    12·2 answers
  • If f(x)=3x-12 what is f(-2)
    13·1 answer
  • If you draw a card with a value of four or less from a standard deck of cards I will pay you $43 if not you pay me $10. Step 1.
    13·1 answer
  • Rose bought 5 pencils for $0.69 each, 3 notebooks for $ 2.75 each, and a pocket dictionary for
    13·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!