To determine the length of the diagonal of a rectangular field measuring 9 meters by 12 meters, we can use the Pythagorean theorem. For a rectangle, the diagonal ($d$) can be found using the formula:

$d = \sqrt{a^2 + b^2}$

where $a$ and $b$ are the lengths of the sides.

Here:

• $a = 9$ meters
• $b = 12$ meters

Substitute these values into the formula:

$d = \sqrt{9^2 + 12^2} = \sqrt{81 + 144} = \sqrt{225} = 15 \text{ meters}$

So, the length of the diagonal, rounded to the nearest meter, is 15 meters.

Would you like more details on this calculation or have any questions?

Related Questions

1. How would the diagonal length change if one of the sides was doubled?
2. What would be the area of this rectangular field?
3. How can the Pythagorean theorem be applied in other real-world contexts?
4. What if the field was a square with sides of 12 meters—how would the diagonal differ?
5. How does the Pythagorean theorem relate to trigonometry?

Tip

The Pythagorean theorem is only applicable to right triangles, making it useful in problems involving diagonals in rectangles and squares.