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 12 miles long and 6 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 \(a=12\), \(b=6\), \(c\) = diagonal.
$$c^2 = a^2 + b^2$$
$$c^2 = 12^2 + 6^2$$

Step2: Calculate squared values

$$c^2 = 144 + 36$$
$$c^2 = 180$$

Step3: Simplify radical

$$c = \sqrt{180} = \sqrt{36 \times 5} = 6\sqrt{5}$$

Step4: Decimal approximation

$$6\sqrt{5} \approx 6 \times 2.236 \approx 13.4$$

Answer:

In simplified radical form, the pedestrian route is \(6\sqrt{5}\) miles long.
The decimal approximation to the nearest tenth is 13.4 miles.