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# Isosceles triangle ABC has two sides with lengths 3 and 9.

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Manager
Joined: 17 Jan 2018
Posts: 87
Concentration: Entrepreneurship, Strategy
Isosceles triangle ABC has two sides with lengths 3 and 9.  [#permalink]

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28 Aug 2018, 22:14
Hi all ,

Q ) Isosceles triangle ABC has two sides with lengths 3 and 9. What is the length of the third side?

The given solution was 9 for the above question, and explaination was given that with 3 - 3 - 9 we cant form an Isosceles triangle , only with 9 - 9 - 3 will form an Isosceles triangle.

But 3 - 3 - 9 will also form the Isosceles triangle right but it may look smaller than the 9 - 9 - 3 ?

or else am i missing something basic here ?
Senior Manager
Joined: 17 Jan 2017
Posts: 298
Location: India
GPA: 4
WE: Information Technology (Computer Software)
Re: Isosceles triangle ABC has two sides with lengths 3 and 9.  [#permalink]

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28 Aug 2018, 22:23
1
henryford wrote:
Hi all ,

Q ) Isosceles triangle ABC has two sides with lengths 3 and 9. What is the length of the third side?

The given solution was 9 for the above question, and explaination was given that with 3 - 3 - 9 we cant form an Isosceles triangle , only with 9 - 9 - 3 will form an Isosceles triangle.

But 3 - 3 - 9 will also form the Isosceles triangle right but it may look smaller than the 9 - 9 - 3 ?

or else am i missing something basic here ?

To determine if the three lengths will form a triangle or not.

We need to know the most basic property of a triangle:

Sum of lengths of any two sides of a triangle > Length of the third side

This means that:

• a + b > c
• b + c > a
• c + a > b

Please note that all the three inequalities should satisfy for the triangle to exist.

For the above Question if the triangle has 3-3-9 as its sides then 3+3 is not greater than 9. Hence triangle can't be formed.
In case of 9-9-3,
9+9>3
9+3>9
3+9>9
Hence a triangle can be formed.
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Re: Isosceles triangle ABC has two sides with lengths 3 and 9.   [#permalink] 28 Aug 2018, 22:23
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