Given the lengths of the three sides of a triangle as $$a$$, $$b$$, and $$c$$, is it possible to construct a triangle with these dimensions? $$ a = 10$$, $$b = 5$$, $$c =4 $$

Flashcard 15 - Quantitative Reasoning Flashcard Set for the DAT

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Explanation:

According to the triangle inequality theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the remaining side. In this case, $10 + 5 > 4$ and $10 + 4 > 5$, but $5 + 4 \ngtr 10$, which violates the triangle inequality theorem. Therefore, it is not possible to construct a triangle with these dimensions.

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