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The midsegment of a triangle is 7.5 , what is the measure of the third side? a. 7.5 b. 3.75 c. 15 d. 10

Ask by Hammond Phillips. in the United States
Jan 22,2025

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Answer

The third side is 15. **Answer:** c. 15

Solution

In a triangle, the **midsegment** (or **midline**) is a line segment that connects the midpoints of two sides of the triangle. According to the **Midsegment Theorem**, the midsegment is **parallel** to the third side and is **half** its length. Given: - **Midsegment length = 7.5** Let the length of the third side be \( x \). According to the theorem: \[ \text{Midsegment} = \frac{x}{2} \] \[ 7.5 = \frac{x}{2} \] \[ x = 2 \times 7.5 = 15 \] **Therefore, the measure of the third side is 15.** **Answer:** c. 15

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Beyond the Answer

Did you know that in any triangle, the midsegment connects the midpoints of two sides and is parallel to the third side? It also has a special property: its length is always half the length of the third side! So if the midsegment is 7.5, just double that, and you’ll find the third side must be 15. That makes option c the answer—math is such a cool detective! When solving for the lengths of sides in triangles, a common pitfall involves forgetting to check if you're working with the right sides or angles. Just like a puzzle, you must piece it all together correctly! Always remember to carefully identify sides and their relationships; it can change everything in your calculations. Keep practicing, and you'll become a triangle pro!

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