Question

NO LINKS!!! URGENT HELP PLEASE!!!! Part 1

For 1, 3, and 5, Determine if the side lengths could form a triangle. Use an inequality to prove your answer.


1. 16 m, 21 m, 39 m


3. 34 km, 27 km, 58 km


5. 12 cm, 12 cm, 25 cm

Answer 1

1. No: 16 + 21 = 37 < 39

2. Yes: 34 + 27 = 61 > 58

3. No: 12 + 12 = 24 < 25

Explanation:

Triangle Inequality Theorem

The sum of the lengths of any two sides of a triangle is greater than the length of the third side.

To determine if the given side lengths could form a triangle, sum the two shortest sides and observe if the sum is greater than the length of the longest side.

Question 1

`\implies 16 + 21 = 37`

As 37 < 39, the sum of the shortest two sides is less than the length of the longest side, and so the given side lengths cannot form a triangle.

Question 3

`\implies 34+27=61`

As 61 > 58, the sum of the shortest two sides is greater than the length of the longest side, the given side lengths can form a triangle.

Question 5

`\implies 12+12=24`

As 24 < 25, as the sum of the shortest two sides is less than the length of the longest side, the given side lengths cannot form a triangle.

Answer 2

1) No, 3) Yes, 5) No

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Use triangle inequality theorem, according to which:

• The sum of the smaller two side lengths must be greater than the longest side.

Q1)

• 16 + 21 = 37 < 39, this is a No

Q3)

• 27 + 34 = 61 > 58, this is a Yes

Q5)

• 12 + 12 = 24 < 25, this is a No