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.MathematicsNCERTStandard VI

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