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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 :

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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.

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