https://file.aiquickdraw.com/mathbot/file/172986286511126h9a5w5.jpg

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.

Find the length of the third side. If necessary, round to the nearest tenth.

Learn how to find the hypotenuse of a right triangle with legs measuring 6 and 9 units using the Pythagorean Theorem. The solution involves applying the formula c^2 = a^2 + b^2 and rounding the result to the nearest tenth. Suitable for students in Grades 6-8.

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