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.

_________________

Only those who risk going too far, can possibly find out how far one can go