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.
