Two sides of a triangle measure 16 and 21 . What is the range of the third side of the triangle

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To determine the possible range for the third side of a triangle when two sides measure 16 and 21, we use the **Triangle Inequality Theorem**. This theorem states that for any triangle, the length of any one side must be: 1. **Less than the sum** of the other two sides. 2. **Greater than the difference** of the other two sides. Let's apply this to your triangle: - **Given:** - Side $$ a = 16 $$ units - Side $$ b = 21 $$ units - Let $$ c $$ be the third side. - **Applying the Triangle Inequality Theorem:** 1. **Upper Bound:** $$ c < a + b $$ $$ c < 16 + 21 $$ $$ c < 37 \text{ units} $$ 2. **Lower Bound:** $$ c > |a - b| $$ $$ c > |16 - 21| $$ $$ c > 5 \text{ units} $$ - **Conclusion:** The third side $$ c $$ must be **greater than 5 units** and **less than 37 units**. - **Range of the Third Side:** $$ 5 < c < 37 \text{ units} $$ **Final Answer:** The third side must be longer than 5 units and shorter than 37 units. In other words, 5 < c < 37. The third side must be greater than 5 units and less than 37 units.

Two sides of a triangle measure 16 and 21 . What is the range of the third side of the triangle

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