SAT Math : How to find the length of the side of an equilateral triangle

Study concepts, example questions & explanations for SAT Math

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Example Questions

Example Question #126 : Geometry

In \(\displaystyle \Delta A B C\)\(\displaystyle AB = 6\) and \(\displaystyle BC = 8\). Which of the following CANNOT be the length of side \(\displaystyle \overline{AC}\)

Possible Answers:

\(\displaystyle 7\)

\(\displaystyle 8\)

\(\displaystyle 1\)

\(\displaystyle 6\)

\(\displaystyle 3\)

Correct answer:

\(\displaystyle 1\)

Explanation:

The sum of the lengths of any two sides of a triangle must be greater than the length of third side.

\(\displaystyle A+B>C\)

Therefore, because 

\(\displaystyle 6 +3 >8\)

\(\displaystyle 6 +6 >8\)

\(\displaystyle 6 +7 >8\)

\(\displaystyle 6 +8>8\)

and

\(\displaystyle 6 +1 < 8\), the correct answer must be \(\displaystyle 1\).

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