Can the sides of a triangle have lengths 1, 10, and 10? Choices: (A)yes (B)no

Check Triangle Inequality Theorem: To determine if these lengths can form a triangle, we need to check the triangle inequality theorem. The 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. Check 1 + 10 > 10: Check if 1 + 10 > 10. Calculation: 1 + 10 = 11, and 11 > 10, so this condition is satisfied. Check 1 + 10 > 10: Check if 1 + 10 > 10. Calculation: 1 + 10 = 11, and 11 > 10, so this condition is satisfied again. Check 10 + 10 > 1: Check if 10 + 10 > 1. Calculation: 10 + 10 = 20, and 20 > 1, so this condition is satisfied too. Confirm Triangle Formation: Since all conditions of the triangle inequality theorem are met, the sides 1, 10, and 10 can indeed form a triangle.

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Can the sides of a triangle have lengths $1$ , $10$ , and $10$ ? $\newline$ Choices: $\newline$ (A) yes $\newline$ (B) no

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Q. Can the sides of a triangle have lengths

1

10

, and

10

\newline

Choices:

\newline

(A) yes

\newline

(B) no

Check Triangle Inequality Theorem: To determine if these lengths can form a triangle, we need to check the triangle inequality theorem. The 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.
Check 1 + 10 > 10: Check if 1 + 10 > 10. Calculation: $1 + 10 = 11$ , and 11 > 10, so this condition is satisfied.
Check 1 + 10 > 10: Check if 1 + 10 > 10. Calculation: $1 + 10 = 11$ , and 11 > 10, so this condition is satisfied again.
Check 10 + 10 > 1: Check if 10 + 10 > 1. Calculation: $10 + 10 = 20$ , and 20 > 1, so this condition is satisfied too.
Confirm Triangle Formation: Since all conditions of the triangle inequality theorem are met, the sides $1$ , $10$ , and $10$ can indeed form a triangle.