Rashi measured two sides of a triangle and found them to be 4 cm and 9 cm. Which of the following could be the length of the third side? 5 cm8 cm13 cm14 cmClear selectionSubmitClear form
Question
Rashi measured two sides of a triangle and found them to be 4 cm and 9 cm. Which of the following could be the length of the third side? 5 cm8 cm13 cm14 cmClear selectionSubmitClear form
Solution
The length of the third side of a triangle, given the lengths of the other two sides, must be less than the sum of the other two sides and greater than the absolute difference of the other two sides. This is known as the triangle inequality theorem.
Here, the given sides are 4 cm and 9 cm.
The sum of these two sides is 4 + 9 = 13 cm. The absolute difference of these two sides is |4 - 9| = 5 cm.
So, the length of the third side must be greater than 5 cm and less than 13 cm.
Therefore, the possible lengths for the third side from the given options are 8 cm.
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