Select the correct answer. A triangle has one side of length 29 units and another of length 40 units. Determine the range in which the length of the third side must lie. A. \( -11

Ask by Evans Welch. in the United States

Mar 17,2025

To find the range of the third side (let's call it \( x \)) of a triangle with two sides of lengths 29 units and 40 units, we can use the triangle inequality theorem. According to this theorem, the sum of the lengths of any two sides must be greater than the length of the remaining side. 1. The first inequality is \( 29 + 40 > x \), which simplifies to \( x < 69 \). 2. The second inequality is \( 29 + x > 40 \), which gives us \( x > 11 \). 3. The third inequality is \( 40 + x > 29 \), which is always true as long as \( x > -11 \). Combining these gives us \( 11 < x < 69 \). Thus, the correct answer is **C. \( 11