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 18 miles long and 9 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: Recall Pythagorean Theorem

For a rectangle with length $l$, width $w$, diagonal $d$: $d^2 = l^2 + w^2$

Step2: Substitute given values

$l=18$, $w=9$, so $d^2 = 18^2 + 9^2$
$d^2 = 324 + 81 = 405$

Step3: Simplify radical for $d$

$d = \sqrt{405} = \sqrt{81 \times 5} = 9\sqrt{5}$

Step4: Calculate decimal approximation

$9\sqrt{5} \approx 9 \times 2.236 \approx 20.1$

Answer:

In simplified radical form, the pedestrian route is $9\sqrt{5}$ miles long.
The decimal approximation to the nearest tenth is 20.1 miles.