Lisadurrett4idn
Answered

Join IDNLearn.com to access a wealth of knowledge and get your questions answered by experts. Whether your question is simple or complex, our community is here to provide detailed and trustworthy answers quickly and effectively.

Which of the following sets of numbers could represent the three sides of a triangle?

Which Of The Following Sets Of Numbers Could Represent The Three Sides Of A Triangle class=

Sagot :

Cb0009idn

Answer:

B-7,22,28

Step-by-step explanation:

The sum of the smaller numbers must be greater than the larger number, if not then the answer is wrong.

Solution:

To classify the given side lengths a triangle, two side lengths must be greater than the third

Example:

Let the given side lengths be AB, BC, and CA.

  • => AB + BC > CA
  • => BC + CA > AB
  • => AB + CA > BC

Verifying each option one by one:

Option A

Given side lengths: 15 units, 27 units, and 43 units

  • 15 + 43 > 27 ⇒ 58 > 27 (True)
  • 27 + 43 > 15 ⇒ 70 > 15 (True)
  • 15 + 27 > 43 ⇒ 42 > 43 (False)

The given side lengths cannot represent a triangle.

Option B

Given side lengths: 7 units, 22 units, and 28 units

  • 7 + 22 > 28 ⇒ 29 > 28 (True)
  • 22 + 28 > 7 ⇒ 50 > 7 (True)
  • 7 + 28 > 22 ⇒ 35 > 22 (True)

The given side lengths can represent a triangle.

Option C

Given side lengths: 14 units, 17 units, and 32 units

  • 14 + 32 > 17 ⇒ 46 > 17 (True)
  • 17 + 32 > 14 ⇒ 49 > 14 (True)
  • 14 + 17 > 32 ⇒ 31 > 32 (False)

The given side lengths cannot represent a triangle.

Option D

Given side lengths: 8 units, 19 units, and 27 units

  • 8 + 27 > 19 ⇒ 35 > 19 (True)
  • 19 + 27 > 8 ⇒ 46 > 8 (True)
  • 8 + 19 > 27 ⇒ 27 > 27 (False)

The given side lengths cannot represent a triangle.

Thus, option B is correct.

We appreciate your participation in this forum. Keep exploring, asking questions, and sharing your insights with the community. Together, we can find the best solutions. Thank you for visiting IDNLearn.com. We’re here to provide accurate and reliable answers, so visit us again soon.