Question

use the pythagorean theorem and the square root property to solve the following problem. express your answer in simplified radical form. then find a decimal approximation to the nearest tenth.
a rectangular park is 8 miles long and 4 miles wide. how long is a pedestrian route that runs diagonally across the park?

in simplified radical form, the pedestrian route is \\(\square\\) miles long.

Explanation:

Step1: Apply Pythagorean Theorem

Let the diagonal be $c$, length $a=8$, width $b=4$.
$$c^2 = a^2 + b^2$$

Step2: Substitute values into formula

$$c^2 = 8^2 + 4^2 = 64 + 16 = 80$$

Step3: Solve for $c$ (simplify radical)

$$c = \sqrt{80} = \sqrt{16 \times 5} = 4\sqrt{5}$$

Step4: Find decimal approximation

$$4\sqrt{5} \approx 4 \times 2.236 \approx 8.9$$

Answer:

In simplified radical form, the pedestrian route is $4\sqrt{5}$ miles long.
The decimal approximation to the nearest tenth is 8.9 miles.