11.8 Pythagorean Theorem Word Problems - Free Printable

You're on the right track! You're trying to find the length of the diagonal of a rectangle with:

- Width = 4 feet
- Length = 10 feet

The diagonal of a rectangle forms a right triangle with the length and width as the two legs. So, we can use the Pythagorean Theorem:

$$
a^2 + b^2 = c^2
$$

Where:
- $ a = 4 $ ft (width)
- $ b = 10 $ ft (length)
- $ c = x $ (diagonal, which we want to find)

---

Step-by-step solution:

1. Plug in the values:
$$
4^2 + 10^2 = x^2
$$

2. Square the numbers:
$$
16 + 100 = x^2
$$

3. Add:
$$
116 = x^2
$$

4. Take the square root of both sides:
$$
x = \sqrt{116}
$$

Now simplify $ \sqrt{116} $:

$$
\sqrt{116} = \sqrt{4 \times 29} = \sqrt{4} \cdot \sqrt{29} = 2\sqrt{29}
$$

So,
$$
x = 2\sqrt{29} \text{ feet}
$$

Or, if you want a decimal approximation:
$$
\sqrt{116} \approx 10.77 \text{ feet}
$$

---

✔ Final Answer:

$$
\boxed{2\sqrt{29}} \text{ feet} \quad \text{or approximately } \boxed{10.77} \text{ feet}
$$

This is the length of the diagonal.