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Can a triangle have sides with the given lengths? Explain 1ft,2 ft ,5 ft

Can a triangle have sides with the given lengths? Explain 1ft,2 ft ,5 ft-example-1
User Sadcow
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1 Answer

10 votes
10 votes

No, because 1 + 2 < 5 contradicts the triangle inequality therem (option C)

Step-by-step explanation:

The triangle inequality theorem states that the sum of any two sides of a triangle must be greater than the length of the third side.

Given the 3 sides as: 1ft, 2 ft, 5 ft

Using the triangle inequality:

1 + 2 > 5

3 > 5 (this is false)

1 + 5 > 2

6 > 2 (this is true)

2 + 5 > 1

7 > 1 (this is true)

There is something else about the theorem, the sum of the two shorter sides should be greater than the sum of the longest side.

In our solution 1+2 > 5 which is false.

Hence, it is not possible to have a triangle with sides 1ft, 2ft and 5 ft because 1 + 2 < 5

The correct option: No, because 1 + 2 < 5 contradicts the triangle inequality therem (option C)

User Annada
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