A 5 mile jogging path diagonal divides a rectangular park in half. The park is 4 miles long. Find the width of the park.

Answer:  The required width of the park is 3 miles.Step-by-step explanation:  Given that a 5 mile jogging path diagonal divides a rectangular park in half and the park is 4 miles long.We are to find the width of the park.As shown in the attached figure below, the diagonal BD divides the rectangle ABCD into two equal parts,where length DA = 5 miles, BD = 4 miles and AB = width = ?Since each angle of a rectangle is right-angle, so triangle ABD will be a right-angled triangle.Using Pythagoras theorem in triangle ABD, we have[tex]BD^2=AB^2+DA^2\\\\\Rightarrow AB=\sqrt{BD^2-DA^2}\\\\\Rightarrow AB=\sqrt{5^2-4^2}\\\\\Rightarrow AB=\sqrt{25-16}\\\\\Rightarrow AB=\sqrt{9}\\\\\Rightarrow AB=3.[/tex]Thus, the required width of the park is 3 miles.