SHOW HOW YOU KNOW if the three lengths can form a triangle. $$ 37,13,21 $$ True False

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1. Let $$ a = 37 $$, $$ b = 13 $$, and $$ c = 21 $$.

2. The triangle inequality states that the sum of any two sides must be greater than the third side. This gives us three conditions:
   - $$ a + b > c $$
   - $$ a + c > b $$
   - $$ b + c > a $$

3. Check the first condition:
   $$
   37 + 13 > 21 \quad \Rightarrow \quad 50 > 21 \quad \text{(True)}
   $$

4. Check the second condition:
   $$
   37 + 21 > 13 \quad \Rightarrow \quad 58 > 13 \quad \text{(True)}
   $$

5. Check the third condition:
   $$
   13 + 21 > 37 \quad \Rightarrow \quad 34 > 37 \quad \text{(False)}
   $$

Since one of the conditions is false, the lengths $$ 37 $$, $$ 13 $$, and $$ 21 $$ cannot form a triangle.

False
The lengths 37, 13, and 21 cannot form a triangle because one of the triangle inequality conditions is not satisfied.

SHOW HOW YOU KNOW if the three lengths can form a triangle. \[ 37,13,21 \] True False

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