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To find the length of the diagonal of a rectangle, given the area and the width, follow these steps:

1. **Calculate the length of the rectangle:**
   - The area \( A \) of the rectangle is given by:
     \[
     A = \text{width} \times \text{length}
     \]
   - Given \( A = 60 \) cm² and the width \( w = 5 \) cm, solve for the length \( l \):
     \[
     60 = 5 \times l
     \]
     \[
     l = \frac{60}{5} = 12 \text{ cm}
     \]

2. **Calculate the length of the diagonal using the Pythagorean theorem:**
   - The diagonal \( d \) of a rectangle can be found using the formula:
     \[
     d = \sqrt{l^2 + w^2}
     \]
   - Substitute the known values:
     \[
     d = \sqrt{12^2 + 5^2}
     \]
     \[
     d = \sqrt{144 + 25}
     \]
     \[
     d = \sqrt{169}
     \]
     \[
     d = 13 \text{ cm}
     \]

Therefore, the length of the diagonal is \( 13 \) cm.

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

Here are some related questions for further practice:
1. What is the perimeter of the rectangle?
2. If the width of the rectangle was doubled, what would be the new area?
3. How does the length of the diagonal change if both the width and length of the rectangle are doubled?
4. What is the length of the diagonal if the width is 7 cm and the area remains 60 cm²?
5. How would you find the area of a rectangle if only the diagonal and width are given?
6. What is the relationship between the sides and diagonal in any rectangle?
7. How do you derive the formula for the diagonal of a rectangle using the Pythagorean theorem?
8. If the length of the rectangle is increased by 2 cm, what will be the new diagonal length?

**Tip:** Always verify the dimensions of the rectangle before solving for the diagonal to ensure accuracy in your calculations.

Learn how to calculate the diagonal of a rectangle given its area and width using the Pythagorean theorem. This problem involves geometry concepts and the application of the Pythagorean theorem in a practical scenario. Suitable for students in Grades 6-8.

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