Question

Sam is visiting a local shopping mall that has a rectangular shape with a diagonal walkway that goes from the entrance of the mall to the food court. The floor plan is shown

1,600
Restroom,
Food Court
Entrance Electronics Sports Store
Store
Sam needs to stop at the sports store on the way to the food court. How much longer, in feet, does he walk than if he walks directly from the entrance to the food court along the diagonal
walkway? Show work to justify your answer.
BI U G X₂
=

Answer 1

262.8 feet

Explanation:

To determine how much longer Sam walks, we need to calculate the distance of his actual path compared to the diagonal walkway. Using the Pythagorean theorem, we can calculate the diagonal walkway's length as follows:

diagonal walkway = √(1600² + 400²) = √(2560000) = 1600√2 ≈ 2,262.8 feet

To find Sam's actual path, we can add the distance from the entrance to the sports store (200 feet) and the distance from the sports store to the food court (800 feet):

actual path = 200 + 800 = 1000 feet

The difference between the actual path and the diagonal walkway is:

1000 - 1600√2 ≈ -262.8 feet

Since the result is negative, it means that Sam walks approximately 262.8 feet less than if he walks directly from the entrance to the food court along the diagonal walkway.