question_answer 8)

Is it possible to have a triangle with the following sides? (i) \[\text{2 cm},\text{ 3 cm},\text{ 5 cm}\]               (ii) \[\text{3 cm},\text{ 6 cm},\text{ 7 cm}\] (iii) \[\text{6 cm},\text{ 3 cm},\text{ 2 cm}.\]                

Answer:

                (i) \[\mathbf{2 cm, 3 cm, 5 cm}\] We have              \[\text{2}+\text{3}=\text{5}\] \[\Rightarrow \] Sum of the lengths of two sides = Length of the third side This is impossible since the sum of the lengths of any two sides of a triangle is greater than the length of the third side. (ii) \[\mathbf{3 cm, 6 cm, 7 cm}\] We see that       \[\text{3}+\text{6}>\text{7}\] \[\text{6}+\text{7}>\text{3}\] \[\text{7}+\text{3}>\text{6}\] Therefore, it is possible to have a triangle with side lengths \[\text{3 cm},\text{ 6 cm},\text{ 7 cm}\]. (iii) \[\mathbf{6 cm, 3 cm, 2 cm}\] We see that      \[\text{6}+\text{3}=\text{9}>\text{2}\] \[\text{3}+\text{2}=\text{5}>\text{ /6}\] \[\text{2}+\text{6}=\text{8}>\text{3}\] Therefore, it is not possible to have a triangle with side lengths \[\text{6 cm},\text{ 3 cm},\text{ 2 cm}\].