Question

a jogger is going running in a rectangular park that is 40 yards by 42 yards. starting from where joggers car is parked in the southeast corner, the jogger runs west along the width of the park and then north along the length. when the jogger reaches the northwest corner, she takes a shortcut straight back to her car. how far does the jogger run in all?

yards

Explanation:

Step1: Calculate first two segments

The jogger runs 40 yards west, then 42 yards north. Sum these distances:
$40 + 42 = 82$ yards

Step2: Find shortcut (diagonal) length

Use Pythagorean theorem for rectangle diagonal:
$$d = \sqrt{40^2 + 42^2} = \sqrt{1600 + 1764} = \sqrt{3364} = 58$$ yards

Step3: Total distance run

Add all three segments:
$82 + 58 = 140$ yards

Answer:

140 yards