Can the sides of a triangle have lengths 5, 5, and 10? Choices: (A)yes (B)no

Check Triangle Inequality Theorem: To determine if these side lengths can form a triangle, we need to use the Triangle Inequality Theorem. This theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. Calculate Side Lengths: Let's check the sides: Sum of two shorter sides: 5 + 5 = 10 Length of the longest side: 10 According to the Triangle Inequality Theorem, 10 should be less than 10 for these to form a triangle. Apply Theorem: Since 10 is not less than 10, but exactly equal, the sides 5, 5, and 10 cannot form a triangle.

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Can the sides of a triangle have lengths $5$ , $5$ , and $10$ ? $\newline$ Choices: $\newline$ (A) yes $\newline$ (B) no

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Q. Can the sides of a triangle have lengths

5

5

, and

10

\newline

Choices:

\newline

(A) yes

\newline

(B) no

Check Triangle Inequality Theorem: To determine if these side lengths can form a triangle, we need to use the Triangle Inequality Theorem. This theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
Calculate Side Lengths: Let's check the sides: $\newline$ Sum of two shorter sides: $5 + 5 = 10$ $\newline$ Length of the longest side: $10$ $\newline$ According to the Triangle Inequality Theorem, $10$ should be less than $10$ for these to form a triangle.
Apply Theorem: Since $10$ is not less than $10$ , but exactly equal, the sides $5$ , $5$ , and $10$ cannot form a triangle.