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Q.

Two sides of a triangle are of lengths 7 cm and 3.5 cm. The length of the third side of the triangle cannot be


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a

     3.6 cm  

b

    4.1 cm  

c

     3.4 cm  

d

     3.8 cm   

answer is C.

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Detailed Solution

Given that the two sides of a triangle are 7 cm and 3.5 cm.
The triangle inequality theorem states that “the sum of the lengths of any two sides of a triangle is greater than the length of the third side”.
Therefore, the length of the third side will be smaller than (7 + 3.5) = 10.5 cm and greater than (7 - 3.5) = 3.5 cm.
In option 1, we have,
3.6>3.5
Therefore, 3.6 cm could be the length of the third side.
In option 2, we have,
4.1>3.5
Therefore, 4.1 cm could be the length of the third side.
In option 4, we have,
3.8>3.5
Therefore, 3.8 cm could be the length of the third side.
In option 3, we have,
3.4≯3.5
Therefore, 3.4 cm could not be the length of the third side.
Thus, the length of the third side can’t be 3.4 cm.
Hence, option (3) is correct.
 
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