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Question

Draw five triangles and measure their sides. Check in each case, if the sum of the lengths of any two sides is always greater than the third side.


Solution

Yes, the sum of two sides of a triangle is always greater than the third side, 
Let us verify it with few examples;
Example(i):
 
Here, we observe that sum of the lengths any two sides is $=5.2+5.2=10.4~cm$ is obviously greater than third side $=5.2~cm$
Hence, verified.
Example(ii): 

Here also, we observe that sum of length the two sides$=17+8=25~cm$ is greater than the third side of length $15~cm$
Hence, verified.
 Example (iii)

Similar way, sum of lengths of of any two sides $9+10=19~cm$ is greater than the third side of length$~15~cm$
 Example (iv):


Similar way, the sum of the lengths any two sides $=8 +5=13~ cm$ is greater than the length of the third side$=5~cm$.
Example (v):

The sum of the lengths of two sides $=25+7=32~cm$   is greater than the length of the third side$=24~cm$.
Hence, for any triangle the sum of two sides of a triangle is always greater than the third side.
Hence, verified.


Mathematics
NCERT
Standard VI

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