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