Questions: State if the following measures can be the sides of a triangle. 11, 7, 20

Transcript text: State if the following measures can be the sides of a triangle. \[ 11,7,20 \]

Solution

Solution Steps

Step 1: Check \( a + b > c \)

We start by checking the first condition of the triangle inequality theorem: \[ 11 + 7 > 20 \] Calculating the left side gives us \( 18 \), which is not greater than \( 20 \).

Step 2: Check \( a + c > b \)

Next, we check the second condition: \[ 11 + 20 > 7 \] Calculating the left side gives us \( 31 \), which is greater than \( 7 \).

Step 3: Check \( b + c > a \)

Finally, we check the third condition: \[ 7 + 20 > 11 \] Calculating the left side gives us \( 27 \), which is greater than \( 11 \).

Conclusion

Since the first condition \( (11 + 7 > 20) \) is not satisfied, the measures \( 11, 7, 20 \) cannot be the sides of a triangle.

Final Answer

The measures \( 11, 7, 20 \) cannot be the sides of a triangle.

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