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Q.

Let the lengths of any two sides of a triangle be 12cm and 15cm, then which of the following will be the range of the third side?


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a

5cm to 40 cm

b

10 cm to 50 cm

c

3 cm to 27 cm

d

8 cm to 46 cm 

answer is C.

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Detailed Solution

It is given that the lengths of any two sides of a triangle are 12cm and 15cm.
We know that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
Therefore, the third side will be less than the sum of these two sides and will be greater than the difference between these two sides.
Calculate the sum of the lengths of any two sides:
12cm+15cm=27cm  
Calculate the difference of the lengths of any two sides:
15cm−12cm=3cm  
Therefore, the third side ranges between 3cm to 27cm.
 and Hence, option (3) is correct.
 
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