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Re: Two sides of an isosceles triangle are 8 and 5 in length, re [#permalink]
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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
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