The triangle in the image appears to be a right triangle, with one side measuring 6 and the other side measuring 9. To find the length of the third side (which would be the hypotenuse in a right triangle), we can apply the Pythagorean theorem:

$c^2 = a^2 + b^2$

Where:

• $c$ is the hypotenuse (the unknown side),
• $a$ and $b$ are the other two sides (6 and 9).

Substituting the given values:

$c^2 = 6^2 + 9^2$ $c^2 = 36 + 81$ $c^2 = 117$ $c = \sqrt{117} \approx 10.8$

So, the length of the third side is approximately 10.8 units, rounded to the nearest tenth.

Would you like further details or have any questions?

Here are 5 related questions for further practice:

1. What would the hypotenuse be if the legs were 8 and 15 instead of 6 and 9?
2. How would you apply the Pythagorean theorem if one side was missing but the hypotenuse was given?
3. If the legs of a triangle are equal, how does this change the calculations?
4. Can the Pythagorean theorem be applied in non-right triangles? Why or why not?
5. What would happen to the length of the hypotenuse if both legs were doubled?

Tip: Always make sure that the triangle is a right triangle before using the Pythagorean theorem.