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Question

# Part of a large wooden art project will be a triangle formed by joining three boards together. The artist has four boards that measure 16 feet, 11 feet. 7 feet, and 3 feet. Which board could not be used with two of the others to form a triangle? (A) the 3-foot board (B) the 7-foot board (C) the 11-foot board (D) the 16-foot board

Solution

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Find the sum of the two sides of the triangle then compare to the third side.

\begin{align*} 16 + 11 & > 7 && {\text {add the two sides and compare to the third side}} \\ 27 & > 7 && {\text {the sum of the two sides is greater than the third side}} \\ \\ 16 + 7 & > 11 && {\text {add the two sides and compare to the third side}} \\ 23 & > 11 && {\text {the sum of the two sides is greater than the third side}} \\ \\ 7 + 11 & > 16 && {\text {add the two sides and compare to the third side}} \\ 17 & > 16 && {\text {the sum of the two sides is greater than the third side}} \end{align*}

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