https://file.aiquickdraw.com/mathbot/file/1727355064090d9r2uwti.jpg

The equation in the image is:

\[
l = \sqrt{r^2 + h^2} = \sqrt{32^2 + 60^2}
\]

This appears to be a variation of the Pythagorean theorem, where \( l \) is the length of the hypotenuse, \( r \) is one leg (32), and \( h \) is the other leg (60). Let's solve for \( l \):

\[
l = \sqrt{32^2 + 60^2} = \sqrt{1024 + 3600} = \sqrt{4624}
\]

Now, calculating the square root:

\[
l = \sqrt{4624} = 68
\]

Thus, \( l = 68 \).

Would you like more details or have any questions? 

Here are five related questions for further exploration:
1. How is the Pythagorean theorem applied in different geometrical contexts?
2. What are some real-life applications of the Pythagorean theorem?
3. How can you derive the formula for the diagonal of a rectangle using the same principle?
4. How do you compute the length of the hypotenuse for other values of \(r\) and \(h\)?
5. How do you find the perimeter and area of a right triangle using this information?

**Tip:** Remember, the Pythagorean theorem only applies to right-angled triangles, where one angle is exactly 90 degrees.

What is the length of the hypotenuse if the base is 32 and the height is 60?

Learn how to calculate the hypotenuse of a right triangle using the Pythagorean theorem, with a base of 32 and height of 60. The solution involves applying the formula l = √(r^2 + h^2). This problem is ideal for students in Grades 7-9.

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