Akshi wrote:
Can't we use the Inequality theorem wherein the sum of two sides should be greater than the third side. Suppose 8 is the third side and sum of the other 2 sides are 5+5=10 (isosceles triangle). Hence proved third side is 8.
Please suggest is the correct way?
Akshi - Yes you can.
|Difference of other 2 sides| < Third side < Sum of other 2 sides
Now the 2 sides of isosceles triangle are 5 and 8
So, we can form 2 triangles with sides 5, 5, 8 and 5, 8, 8
Check if both the triangles satisfy the above condition/inequality:
For
5, 5, 8|5 - 5| < 8 < 5 + 5 [True]
|8 - 5| < 5 < 8 + 5 [True]
Col. A < Col. B
For
5, 8, 8|8 - 5| < 8 < 8 + 5 [True]
|8 - 8| < 5 < 8 + 8 [True]
Col. A = Col. B
This means both 5 and 8 can be the third side of the isosceles triangle.
Hence, option D