Question

a city planner is designing a diagonal biking trail across a rectangular field that is 4 miles long and 2 miles wide. how long will the diagonal biking trail be? express your answer as a simplified square root. 2√10 miles long 6 miles long 2√3 miles long

Explanation:

Step1: Apply Pythagorean theorem

Let diagonal = $d$, length = $4$, width = $2$.
$d^2 = 4^2 + 2^2$

Step2: Calculate squares

$d^2 = 16 + 4 = 20$

Step3: Simplify square root

$d = \sqrt{20} = 2\sqrt{5}$ (Note: The first option in the image likely has a typo; $2\sqrt{5}$ is the correct simplified form.)

Answer:

2√5 miles long

(Note: Assuming the first option in the image may have a typo, the correct simplified square root is $2\sqrt{5}$. If forced to choose from the visible options, but since $2\sqrt{5}$ is not listed, there might be an error in the provided options. However, based on calculation, the answer is $2\sqrt{5}$.)