https://file.aiquickdraw.com/mathbot/file/1726763662382dvv94o7p.jpg

The triangle in the image is a right triangle, with both legs measuring 1 unit each. To find the exact length of the hypotenuse, we can use the Pythagorean theorem:

\[
c = \sqrt{a^2 + b^2}
\]

Where:
- \(a = 1\) unit (one leg),
- \(b = 1\) unit (the other leg),
- \(c\) is the hypotenuse.

Substitute the values:

\[
c = \sqrt{1^2 + 1^2} = \sqrt{1 + 1} = \sqrt{2}
\]

Thus, the exact length of the hypotenuse is:

\[
\boxed{\sqrt{2}}
\]

Would you like more details, or do you have any questions?

Here are some related questions to expand on this concept:
1. What is the decimal approximation of \(\sqrt{2}\)?
2. How does the Pythagorean theorem apply to non-right triangles?
3. What are other common right triangles with known side lengths?
4. Can the hypotenuse ever be shorter than one of the legs in a right triangle?
5. What is the significance of a 45-45-90 triangle?

**Tip:** When solving triangles, it's useful to remember common Pythagorean triples like \(3, 4, 5\) and \(5, 12, 13\).

Find the exact length of the triangle's hypotenuse, given that both legs are 1 unit long.

Learn how to find the hypotenuse of a right triangle with both legs measuring 1 unit. Using the Pythagorean theorem, this solution explains how to calculate the exact length of the hypotenuse as √2. Suitable for students in Grades 6-8.

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