https://file.aiquickdraw.com/mathbot/file/17274743585586o2yv2pu.jpg

To find the length of the third side in a right triangle, we can use the **Pythagorean theorem**. The formula is given by:

\[
a^2 + b^2 = c^2
\]

where \(a\) and \(b\) are the lengths of the legs of the triangle, and \(c\) is the hypotenuse. 

From the diagram:
- One leg is 2 units.
- The other leg is 3 units.

Since these two sides are the legs of the right triangle, we want to find the hypotenuse:

\[
2^2 + 3^2 = c^2
\]

Calculating:

\[
4 + 9 = c^2
\]
\[
13 = c^2
\]

Taking the square root of both sides:

\[
c = \sqrt{13}
\]

So, the length of the third side (the hypotenuse) in simplest radical form is:

\[
\sqrt{13}
\]

Would you like more details or have any questions?

### Related Questions:
1. What is the Pythagorean theorem, and where does it apply?
2. How do you identify the hypotenuse in a right triangle?
3. Can the Pythagorean theorem be used in non-right triangles?
4. What are some examples of Pythagorean triples?
5. What is the distance formula in the coordinate plane?

### Tip:
The Pythagorean theorem only works for **right triangles**—so always make sure the triangle has a right angle before applying it!

Find the length of the third side in a right triangle where the two given sides are 2 and 3 units.

Learn how to find the length of the hypotenuse in a right triangle using the Pythagorean theorem, with sides of length 2 and 3. The solution is provided in simplest radical form, √13. Suitable for students in Grades 7-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation