What type of triangle is formed with side lengths 6, 8, and 10, and how can we determine its properties?

Identifying the Triangle

Given the side lengths of 6, 8, and 10, we can first determine the type of triangle by applying the Pythagorean theorem, which states:

a² + b² = c²

In this case, let’s assign:

• a = 6
• b = 8
• c = 10

Now, we can calculate:

6² + 8² = 36 + 64 = 100

10² = 100

Since both sides of the equation are equal, the triangle with side lengths of 6, 8, and 10 is a right triangle.

Properties of the Triangle

This triangle has several notable properties:

• Right Angle: One of its angles measures 90 degrees, which is characteristic of right triangles.
• Hypotenuse: The longest side, which is 10, acts as the hypotenuse.
• Legs: The other two sides, 6 and 8, are known as the triangle’s legs.

Calculating the Area

To find the area of this triangle, we can use the formula for the area of a right triangle:

Area = (1/2) × base × height

Here, we can consider one leg as the base and the other as the height:

Area = (1/2) × 6 × 8 = 24

Thus, the area of this triangle is 24 square units.

Conclusion

In summary, a triangle with side lengths of 6, 8, and 10 is a right triangle with specific properties making it easy to calculate its area and understand its geometric significance.