uadratic Equations
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 24 miles long and 8 miles wide. How long is a pedestrian route that runs diagonally across the park?
In simplified radical form, the pedestrian route is miles long.

Step 1 ：Given the length and width of the rectangle as 24 miles and 8 miles respectively, we can use the Pythagorean theorem to find the length of the diagonal (c). The Pythagorean theorem is given by \(a^2 + b^2 = c^2\)

Step 2 ：Substitute the given values into the equation: \((24 miles)^2 + (8 miles)^2 = c^2\)

Step 3 ：Calculate the squares: \(576 miles^2 + 64 miles^2 = c^2\)

Step 4 ：Add the squares: \(640 miles^2 = c^2\)

Step 5 ：Take the square root of both sides to solve for c: \(c = \sqrt{640} miles\)

Step 6 ：Simplify the square root: \(c = 8\sqrt{10} miles\)

Step 7 ：To find a decimal approximation to the nearest tenth, calculate the square root of 10, multiply by 8, and round to the nearest tenth: \(8 * \sqrt{10} \approx 25.3 miles\)

Step 8 ：\(\boxed{c \approx 25.3 miles}\)