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 30 miles long and 10 miles wide. how long is a pedestrian route that runs diagonally across the park?
in simplified radical form, the pedestrian route is miles long.

Explanation:

Step1: Apply Pythagorean Theorem

Let the length of the rectangle be $a = 30$ miles, the width be $b = 10$ miles, and the diagonal be $c$. According to the Pythagorean Theorem $a^{2}+b^{2}=c^{2}$. So $c^{2}=30^{2}+10^{2}$.
$c^{2}=900 + 100=1000$.

Step2: Solve for $c$ using square - root property

$c=\sqrt{1000}$. Simplify $\sqrt{1000}=\sqrt{100\times10}=10\sqrt{10}$ miles.

Step3: Find decimal approximation

$\sqrt{10}\approx3.2$, so $10\sqrt{10}\approx10\times3.2 = 31.6$ miles.

Answer:

In simplified radical form, the pedestrian route is $10\sqrt{10}$ miles long.
As a decimal approximation to the nearest tenth, it is $31.6$ miles long.