https://r2.erweima.ai/mathbot/image/1726277019595eoqwiudr.jpg

The image presents a triangle \( \triangle SOW \) where you are asked to find the perimeter. Here’s what we know from the diagram:

- Segment \( SN = 8 \)
- Segment \( SO = 10 \)
- Segment \( ON = 6 \), which is a perpendicular height from point \( O \) to the base \( SW \)

We can use the Pythagorean theorem to find the length of side \( OW \). Since \( ON \) is the height and it forms a right triangle with \( OW \) and \( WN \), we need to calculate \( WN \) first.

Using the relationship \( SW = SN + WN \), where \( SW = 8 \) and the right triangle is \( ONW \), we apply the Pythagorean theorem to find \( OW \).

Let’s calculate \( OW \).The perimeter of triangle \( \triangle SOW \) is 26.0 units.

Would you like further explanation or clarification?

Here are 5 related questions to deepen your understanding:

1. How would the perimeter change if side \( SO \) was longer?
2. Can you apply the Pythagorean theorem to any triangle, or just right triangles?
3. How would you find the area of triangle \( SOW \)?
4. What is the significance of point \( N \) being a right angle in this problem?
5. How could trigonometry be used to solve for \( OW \) without the Pythagorean theorem?

**Tip:** In right triangles, the Pythagorean theorem is a powerful tool for finding unknown sides when two sides are known.

Halla el perímetro de \( \triangle SOW \). Se proporcionan las longitudes de los lados \( SN = 8 \), \( SO = 10 \), y \( ON = 6 \), que es la altura desde el punto \( O \) hacia la base \( SW \). Encuentra el perímetro del triángulo utilizando los datos disponibles.

Aprende a calcular el perímetro de \( \triangle SOW \) utilizando el Teorema de Pitágoras. Este problema incluye conceptos clave de geometría y el uso del teorema para encontrar longitudes desconocidas. Ideal para estudiantes de grados 8 a 10.

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